Share
Solve for a^4+b^4+c^4 Given a+b+c, a^2+b^2+c^2, and a^3+b^3+c^3
Published on July 24, 2026
Algebra
This problem requires finding the sum of fourth powers of three variables, given the sums of their first, second, and third powers. It is solved using Newton's sums and elementary symmetric polynomials.
Question
Answer
To solve the given problem, we are provided with a system of equations involving
We need to find the value of
Step 1: Find the elementary symmetric polynomials
Let the elementary symmetric polynomials be:
From equation (1), we have:
Using the identity
Next, we use the Newton’s Sum identity for
Substitute the known values:
Substitute the known values:
Step 2: Use Newton’s Sums to find
Let
For
Substitute the values we have found:
Alternatively, we can use the identity:
We need
We know
We need
We know
Now substitute back into the squared sum formula:
The value of