Find the sum of the squares of all real numbers, *x*, satisfying the equation

x^{256}– 256^{32}= 0.

- 8
- 128
- 512
- 65,536
- 2(256
^{32})

*x*^{256} – 256^{32} = *x*^{256} – (2^{8})^{32} = *x*^{256} – 2^{256} = 0.

Since 256 is even, we can repeatedly (8 times altogether) factor the difference of squares, to find that the only real solutions to the equation are *x* = 2 and *x* = -2. Then 2^{2} + (-2)^{2} = 8.

The answer is a.