Find the sum of the squares of all real numbers, x, satisfying the equation
x256 – 25632 = 0.
- 8
- 128
- 512
- 65,536
- 2(25632)
x256 – 25632 = x256 – (28)32 = x256 – 2256 = 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 22 + (-2)2 = 8.
The answer is a.