If X+Y+Z=15 and 1/x+1/y+1/z=0, then what is X^2+Y^2+Z^2?

1/X+1/Y+1/X=0

X+Y+Z=15

What is X^2+Y^2+Z^2?

1 Answer
Apr 29, 2017

X^2+Y^2+Z^2 =225

Explanation:

1/X +1/Y+1/Z =0 or (YZ+ZX+XY)/(XYZ)=0 or (YZ+ZX+XY)=0

(X+Y+Z)^2= X^2+Y^2+Z^2 + 2(XY+YZ+ZX) or
15^2=X^2+Y^2+Z^2 + 2*0 or
X^2+Y^2+Z^2 =225 [Ans]