To solve this equation, we can expand the expressions inside the parentheses and combine like terms:
[(x + 1)^4] + [(x - 4)^4] = 9(x^4 + 4x^3 + 6x^2 + 4x + 1) + (x^4 - 8x^3 + 16x^2 - 64x + 256) = 92x^4 - 4x^3 + 22x^2 - 60x + 257 = 97
Now, we have a fourth degree polynomial equation. We can try to simplify this equation further by moving all terms to one side:
2x^4 - 4x^3 + 22x^2 - 60x + 257 - 97 = 2x^4 - 4x^3 + 22x^2 - 60x + 160 = 0
Unfortunately, this polynomial cannot be easily factored. Therefore, a numerical or approximation method such as the Newton-Raphson method or graphing the equation would be needed to find the roots of this polynomial equation.
To solve this equation, we can expand the expressions inside the parentheses and combine like terms:
[(x + 1)^4] + [(x - 4)^4] = 9
(x^4 + 4x^3 + 6x^2 + 4x + 1) + (x^4 - 8x^3 + 16x^2 - 64x + 256) = 9
2x^4 - 4x^3 + 22x^2 - 60x + 257 = 97
Now, we have a fourth degree polynomial equation. We can try to simplify this equation further by moving all terms to one side:
2x^4 - 4x^3 + 22x^2 - 60x + 257 - 97 =
2x^4 - 4x^3 + 22x^2 - 60x + 160 = 0
Unfortunately, this polynomial cannot be easily factored. Therefore, a numerical or approximation method such as the Newton-Raphson method or graphing the equation would be needed to find the roots of this polynomial equation.