Giant Difference of Squares

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

x256 – 25632 = 0.

  1. 8
  2. 128
  3. 512
  4. 65,536
  5. 2(25632)


Show/Hide Solution

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.

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