Problem:
The sum 35+213+35−213 equals
Answer Choices:
A. 23
B. 4365
C. 21+613
D. 32
E. none of these
Solution:
Let a=35+213,b=35−213 and x=a+b. Then
x3=a3+3a2b+3ab2+b3x3=a3+b3+3ab(a+b)x3=10+33−27x
The last equation is equivalent to x3+9x−10=0, or (x−1)(x2+x+10)=0, whose only real solution is x=1.