Math POTW for Secondary and High School Students Forum

POTW Inequality of Positive Real Numbers: Proving (1-1/x^2)(1-1/y^2)≥9 with x+y≤1
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12
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1K
POTW Integer n: Solving the Equation ##\dfrac{n^2+3}{2n+4}## for Integers
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14
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1K
POTW Solve 3-Variable Equation with Real Solutions | √(z-y^2-6x-26)+x^2+6y+z-8=0
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3
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878
MHB How Can You Minimize This Complex Square Root Expression for Positive x and y?
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6
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1K
POTW Prove that the roots of a polynomial cannot be all real
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5
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1K
MHB Can x(x+y) Be Proved to Be ≤ 2 for Positive Real Numbers?
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11
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1K
POTW Proving Inequality between Positive Real Numbers a and b: a(a+b) ≤ 2
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6
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930
MHB Maximize (x1+x2)(x1+x3)x4 for Quartic Equation with Real Roots in [1/2,2]
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2
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946
POTW Find Triplets of Positive Integers with Sum of Cubes
2
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66
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3K
MHB Can You Verify This Trigonometric Identity Involving Cosecant Functions?
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1
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929
MHB What Is the Minimum Value of (a²+b²)/c² in Triangle ABC?
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1
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876
POTW Find the Sum of Two Real Numbers | Solve a + b with Given Equations
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19
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1K
MHB Is the product of two radical expressions equal to six?
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13
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1K
POTW Finding the Product of Real Roots: POTW Equation Solution
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9
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1K
MHB What Is the Maximum Value of \( x \) in the Equation \( 2x+y+\frac{4}{xy}=10 \)?
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7
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1K
MHB What Is the Minimum Cosine Value in Trigonometric Constraints?
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2
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904
MHB How Can We Find All Integer Pairs (k, n) That Satisfy This Factorial Equation?
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4
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1K
MHB What is the minimum value of a+b+c+d if a^2-b^2+cd^2=2022?
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5
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991
MHB Minimum Value of (a+7)^2+(b+2)^2 with Constraint (a-5)^2+(b-7)^2=4 - POTW #506
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5
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900
MHB Minimum Sum of Non-Negative Integers with Given Equation - POTW #504
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1
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791
MHB Can $\sin^5 x + \cos^3 x$ Equal 1?
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1
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1K
MHB Can This Infinite Product Surpass 50?
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1
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776
MHB Can This Triangle Configuration Prove a Right Angle?
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1
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866
MHB Can You Prove the Polynomial Has Three Distinct Roots?
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1
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682
MHB Can $2^{\sqrt{12}}$ Exceed 11?
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2
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926
MHB What is the Range of $w(w+x)(w+y)(w+z)$ When $x+y+z+w=x^7+y^7+z^7+w^7=0$?
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1
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822
MHB Can Both Solutions of This Quadratic Equation Be Perfect Squares?
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1
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825
MHB How many positive integral solutions $(x,\,y)$ are there for the equation $\dfrac{1}{x+1}+\dfrac{1}{y}+\dfrac{1}{y(x+1)}=\dfrac{1}{2015}$?
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1
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755
MHB What is the greatest 5-digit palindrome for 7n to be a 6-digit palindrome?
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1
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773
MHB How do you solve a system of equations with rational functions?
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1
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951
MHB Prove $0\le xy+yz+zx-2xyz\le7/27$ for $x+y+z=1$
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1
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787
MHB Can You Simplify This Trigonometric Expression?
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1
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728
MHB How Does Solving P(x) Influence Q(x^2)?
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1
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745
MHB Can You Prove This Inequality with Positive Real Numbers?
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1
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835
MHB How Do You Evaluate the Product of g(x) at the Roots of a Quintic Polynomial?
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1
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761
MHB Sum of Cosine Values for $x$ | POTW #480 8/24/2021 | $100^{\circ}<x<200^{\circ}$
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1
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910
MHB What is the value of (x+y)(y+z)(z+x) if 1/(x+y+z) = 1/x + 1/y + 1/z?
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1
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780
MHB Find All Positive Integer Pairs for (x, y) in sqrt[3]{7x^2-13xy+7y^2}=|x-y|+1
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1
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837
MHB How to Evaluate the Expression for Roots of the Polynomial in POTW #476?
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1
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803
MHB What is the solution for evaluating $ab+cd$ with given constraints in POTW #477?
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1
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743
MHB Can You Solve This Unique Fraction Challenge?
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1
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791
MHB Can you solve this week's POTW #474: Four real numbers with unique permutations?
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1
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809
MHB What Is the Largest Natural Number $n$ Such That $2^n$ Divides $3^{2016}-1$?
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1
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909
MHB Discover the Area of Points in a Unit Square | POTW #471
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1
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755
MHB How Many Integer Solutions Exist for the Equation |x|+|y|+|z|=2010?
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2
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758
MHB Prove Inequality: Integral of Square Root vs. Trigonometric Function
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1
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745
MHB Find Functions Satisfying $f^d(x)=2015-x$ for All Divisors of 2015
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1
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754
MHB Can $(n^2+11n-4) \cdot n! + 33 \cdot 13^n + 4$ Be a Perfect Square?
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2
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787
MHB What is the Time Estimate for Completing a 1000-Piece Jigsaw Puzzle?
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1
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856
MHB Finding Extremes of x^3+y^3+z^3+xyz for Real Numbers with Constraints
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1
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726
MHB Can You Solve This Week's Challenging System of Equations?
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1
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808
MHB Which Prime Numbers Make $2p^3 + 4p^2 - 3p + 12$ a Fifth Power?
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1
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1K
MHB Is Every Positive Real Number a Solution to (x+1)(x+2)(x+5)≥36x?
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1
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867
MHB What Are the Possible Values of c for a Triangle with Area 5?
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1
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728
MHB Can All Outputs of a Quadratic Function Be Integers?
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1
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830
MHB Can Non-zero Polynomials with Real Coefficients Have Real Roots in Common?
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1
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843
MHB Is it possible to find 6-digit numbers with a sum of 8?
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1
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865
MHB Possible Values: $f(8765)-f(4321)$ for Functions Satisfying Inequalities
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1
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765
MHB How Do You Solve POTW #456 for (x+20)(y+20)(z+20)?
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1
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793
MHB Can You Solve the Integer System xz-2yt=3 and xt+yz=1?
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1
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908
MHB What is the Greatest Value of an Expression with Given Numbers and Equation?
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1
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850
MHB Integer Solutions for Equation: POTW #453 - Feb 1st, 2021
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1
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894
MHB Can You Solve This Integer Equation for January 25th, 2021?
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3
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905
MHB How Many Divisors of $30^{2003}$ Are Not Divisors of $20^{2000}$?
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1
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813
MHB What are the solutions to x^3+3367=2^n?
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1
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1K
MHB Triangle ABC: Find Possible Values of Cos A | POTW #449 Jan 4th 2021
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2
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809
MHB How to Tackle the Latest POTW Inequality Challenge?
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2
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841
MHB Can You Solve for a and b in This Trigonometric Equation?
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1
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756
MHB Triangle with Complex Number Vertices SATISFIES Equilateral Relation
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1
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826
MHB Proof of Regular Heptagon Ratio: AD^3/AB^3 - (AB+2AC)/(AD-AC) = 1
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1
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852
MHB Maximum Value of Square Root Expression with Three Variables in [0,1]
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2
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1K
MHB How Many Non-Congruent Triangles with Integer Sides Can a Given Perimeter Form?
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1
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822
MHB Is Sine of x Greater Than or Equal to 2x Over Pi for Angles Up to Pi/2?
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1
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844
MHB Can You Solve the Convex Quadrilateral Angle Mystery?
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2
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959
MHB Can All Roots of This Cubic Equation Be Bounded by 1?
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1
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814
MHB Is the Expression an Integer When Rational Conditions Apply?
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1
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785
MHB Can You Prove These Inequalities for Real Numbers a, b, and c?
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2
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845
MHB What are the solutions to a set of equations involving triple real numbers and specific conditions?
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1
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842
MHB Is It Possible to Prove Real Root Properties in Cubic Equations?
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1
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916
MHB What Is the Value of b If All Roots of the Polynomial Are Positive Real Numbers?
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2
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863
MHB Quadratic Polynomial Problem: Proving Equality with Real Numbers
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1
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881
MHB Solution to Problem #433: Proving a+b+c=0 yields 9
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1
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838
MHB How Many Final Points Can Be Reached in a Ten-Step Lattice Walk?
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1
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833
MHB How Do Divisors Relate in POTW #431's Integer Equation?
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1
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920
MHB Which Integers Make All Roots of This Polynomial Integer?
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1
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844
MHB How Do You Calculate the Sum of Sides and Diagonals of a Regular 12-Gon?
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1
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819
MHB How Can a Fifth Degree Polynomial Meet Specific Divisibility Conditions?
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2
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918
MHB Challenge: Find the Positive Integer for $133^5$ + $110^5$ + $84^5$ + $27^5$
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1
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973
MHB The value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$ is 1234.
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1
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899
MHB Can You Solve This Complex Radical Equation?
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1
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859
MHB Maximizing a in $ax^3+bx^2+cx+d$ with Constraints | POTW #424 07/06/2020
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1
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934
MHB How to Calculate the Sum of Squares in Complex Equation Systems?
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1
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885
MHB Problem #422: Four Non-Negative Real Numbers and a Unique Condition
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1
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942
MHB What Natural Numbers Solve the Equation from POTW #421?
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1
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958
MHB Find the Sum of Real Numbers Satisfying Equations
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1
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946
MHB What Is the Probability That a Bridge Is Empty at Noon?
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1
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947
MHB Can you solve this week's POTW: Integrating a Complex Expression? May 25th, 2020
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1
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931
MHB Acute Triangle ABC: Point P and Line Intersections Formula
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1
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820
MHB Can You Solve These Unique System of Equations?
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1
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1K
MHB How Can One Non-Real Root Be Guaranteed in Equation #416?
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1
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1K
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POTW High School

Welcome to the High School POTW forum!

Math problems will be posted each week on Monday, most likely early in the morning (1am, 2am, etc.) Eastern Standard Time. There will be one math problem each week at the advanced high school student or secondary level.

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