Problem: Find the sum of the squares of all real numbers satisfying the equation
x256−25632=0
Answer Choices:
A. 8
B. 128
C. 512
D. 65536
E. 2(25632)
Solution:
Since
x256−25632=x(28)−(28)32=x(28)−2(28)=(x(27)+2(27))(x(26)+2(26))⋯(x+2)(x−2)
the sum of the squares of the real roots is 8.