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+33−27​x​
The last equation is equivalent to x3+9x−10=0, or (x−1)(x2+x+10)=0, whose only real solution is x=1.