Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

In summary, an algebraic equation is a mathematical statement that contains variables and operations, and the goal is to find the values of the variables that make the equation true. To solve an algebraic equation, you must isolate the variable by using inverse operations. The degree of an algebraic equation is the highest exponent in the equation. This algebraic equation can have more than one solution. To check if the solutions are correct, you can substitute them back into the equation and solve it, or graph the equation and see if the solutions lie on the graph.
  • #1
anemone
Gold Member
MHB
POTW Director
3,883
115
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.
 
Mathematics news on Phys.org
  • #2
anemone said:
Factorize $x^4+y^4+z^4-xyz(x+y+z)$.

is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients
 
  • #3
kaliprasad said:
is the question correct (that is I am missing something)

$x^4+y^4+z^4-xyz(x+y+z) = x^4-x^2yz - xyz(y+z) + y^4+z^4$ if we put in descending power of x and $y^4+z^4$ does not factor over real coefficients

Ops...it was my mistake to post an incorrect problem...the problem should read:

Find the sum of square factorization for $x^4+y^4+z^4-xyz(x+y+z)$.

Sorry for causing the confusion, folks!:eek:
 
  • #4
needs closure.
 

Related to Solve Algebraic Equation: x⁴+y⁴+z⁴-xyz(x+y+z)

1. What is an algebraic equation?

An algebraic equation is a mathematical statement that contains one or more variables and a set of operations, such as addition, subtraction, multiplication, and division. The goal is to find the values of the variables that make the equation true.

2. How do you solve an algebraic equation?

To solve an algebraic equation, you must isolate the variable on one side of the equation by using inverse operations. The goal is to get the variable by itself on one side and all other terms on the other side. Once the variable is isolated, you can substitute the solutions back into the equation to check if it is true.

3. What is the degree of this algebraic equation?

The degree of an algebraic equation is the highest exponent in the equation. In this equation, the degree is 4, as all the terms have an exponent of 4.

4. Can this algebraic equation have more than one solution?

Yes, this algebraic equation can have more than one solution. In fact, most algebraic equations have more than one solution, unless they are identities or contradictions. In this case, there are infinite solutions as there are three variables and only one equation.

5. How can I check if my solutions are correct for this algebraic equation?

You can check your solutions by substituting the values back into the equation and solving it. If the equation is true with the given values, then the solutions are correct. You can also graph the equation and see if the solutions lie on the graph.

Similar threads

MHB Prove Divisibility: $(x-y)^2+(y-z)^2+(z-x)^2=xyz$ yields $x^3+y^3+z^3$
    • General Math
Replies
1
Views
945
MHB Find Maximum of xyz: Real Solutions
    • General Math
Replies
1
Views
595
I Adding 'z' to 2D graph equation
    • General Math
Replies
3
Views
1K
B Have I proved some part of Fermat's last theorem?
    • General Math
Replies
15
Views
1K
MHB Challenge Problem #7: Σ(x/(y^3+2))≥1
    • General Math
Replies
2
Views
1K
MHB What is the Sum of x, y, and z in a Non-Negative Real Number System?
    • General Math
Replies
4
Views
980
MHB Show x³y+y³z+z³x is a constant
    • General Math
Replies
1
Views
866
MHB Inequality involves radical, square and factorial expression 3√{x}+2y+1z^2⩽ 13
    • General Math
Replies
6
Views
1K
B Inverse Functions: Why rewrite as y=f(x) ?
    • General Math
Replies
11
Views
566
MHB Factorize 6(x^5+y^5+z^5)-5(x^2+y^2+z^2)(x^3+y^3+z^3)
    • General Math
Replies
1
Views
770

Hot Threads

Recent Insights

Back
Top