Solve math equation without assumptions

In summary: Maths factorization problem!It doesn't really help. A solution is to reduce everything to a 6-th order algebraic equation (either in "a" or in "b") to which you know that 3 and 4 are solutions. You can reduce the degree to 4 then and to a 4-th order algebraic equation, the exact solutions do exist. All 4 of them are complex (with nonzero imaginary part)...
  • #1
Milind_shyani
42
0
One mathematical sum is harassing me since a few days the problem is;:-
a^2+b^2=25 and a^3+b^3=91. find the value of a and b.
Now here we cannot take that into consoderation that as a^2+b^2=25 , a=3 and b=4. But we have to find the answer without any assumtions.May i please get the answer as soon as possible
 
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  • #2
In which set of numbers do you search the solution to your system of equations...?

Daniel.

P.S. This is NOT "Advanced Physics".
 
  • #3
Forget the location. Let me help you.
a^3 + b^3 = (a+b)(25-ab)
Put a + b = x.
Then ab = [(a+b)^2 - (a^2 + b^2)]/2 = (x^2 - 25)/2
 
  • #4
It doesn't really help. A solution is to reduce everything to a 6-th order algebraic equation (either in "a" or in "b") to which you know that 3 and 4 are solutions. You can reduce the degree to 4 then and to a 4-th order algebraic equation, the exact solutions do exist. All 4 of them are complex (with nonzero imaginary part)...

That's why i asked about the set in which you want to determine the solutions...

Daniel.
 
  • #5
Just guess! There are only a few numbers that a and b even have a chance of being. In fact, there is really only one pair of numbers that could work.
 
  • #6
Milind_shyani said:
One mathematical sum is harassing me since a few days the problem is;:-
a^2+b^2=25 and a^3+b^3=91. find the value of a and b.
Now here we cannot take that into consoderation that as a^2+b^2=25 , a=3 and b=4. But we have to find the answer without any assumtions.May i please get the answer as soon as possible
Why do I hate people who double post so much!
Why must you post one problem in two different threads in only one board? Why?
Maths factorization problem!
dextercioby said:
It doesn't really help. A solution is to reduce everything to a 6-th order algebraic equation (either in "a" or in "b") to which you know that 3 and 4 are solutions. You can reduce the degree to 4 then and to a 4-th order algebraic equation, the exact solutions do exist. All 4 of them are complex (with nonzero imaginary part)...

That's why i asked about the set in which you want to determine the solutions...

Daniel.
In fact, it can be reduced to a cubic equation. :)
 
Last edited:

Related to Solve math equation without assumptions

1. How can I solve a math equation without making any assumptions?

There are several methods for solving math equations without assumptions, such as substitution, elimination, and graphing. However, the most important step is to carefully analyze the equation and determine what information is given and what information is needed to find the solution. This will help guide your approach and avoid making any unnecessary assumptions.

2. Can I always solve a math equation without making assumptions?

No, in some cases it may not be possible to solve a math equation without making at least one assumption. This is because some equations may have multiple solutions, or may require more information than what is given in order to find a unique solution. In these cases, making a reasonable assumption can help lead to a solution.

3. What are some common assumptions that are made when solving math equations?

Some common assumptions include assuming a variable has a certain value, assuming a certain relationship between variables, or assuming a certain pattern in a sequence. These assumptions can help simplify the equation and make it easier to solve, but it is important to be aware of them and consider their potential impact on the solution.

4. Can assumptions affect the accuracy of the solution to a math equation?

Yes, assumptions can definitely affect the accuracy of the solution. Making incorrect assumptions can lead to an incorrect solution, while making reasonable assumptions can lead to a more accurate solution. It is important to be aware of the assumptions being made and to evaluate their impact on the solution.

5. How can I check if my solution to a math equation is correct?

To check if a solution to a math equation is correct, you can plug the solution into the original equation and see if it satisfies the given conditions. You can also use a calculator or online tool to double check the solution. Additionally, it may be helpful to ask someone else to check your work or to try solving the equation using a different method to see if you get the same answer.

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