Scratching my head at this problem...?

Question

If f(x)=x^2+2 find the sum and differences of the roots (solutions) of the equation: f(f(x) + 3f(x) = xf(x) + f(x).

10 points for best answer! (Please show work)!

Answer 1

Anyone who gets sucked in by Jammy J deserves to be scammed.

f(f(x)) = f(x)*(x + 1 - 3) = f(x)*(x - 2) gives us
(f(x))^2 + 2 = (x^2 + 2)*(x - 2) = (x^2 + 2)^2 + 2 = x^3 - 2x^2 + 2x - 4, or x^4 + 4x^2 + 4 + 2 = x^3 - 2x^2 + 2x - 4. which simplifies to

x^4 - x^3 + 6x^2 - 2x + 10 = 0.

From "relations on the roots," we know that the sum of the roots is the negative of the coefficient of x^3, so the sum of the roots is 1.

The other part of the question is not clear. There are four roots, say a, b, c, d. What do you mean by the difference of the roots? Is it a - b + c - d, or a + b - c - d, or a + b + c - d, or ... ? Do you see the problem?