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​.