Problem:
If xy=a,xz=b, and yz=c, and none of these quantities is 0 , then x2+y2+z2 equals
Answer Choices:
A. abcab+ac+bc
B. abca2+b2+c2
C. abc(a+b+c)2
D. abc(ab+ac+bc)2
E. abc(ab)2+(ac)2+(bc)2
Solution:
Observe that abc=x2y2z2=x2c2, so x2=cab. Likewise, y2=bac and z2=abc. So
x2+y2+z2=cab+bac+abc=abc(ab)2+(ac)2+(bc)2.