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

Question

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

X+Y+Z=15

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

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Answer 1 · 2017-04-29T10:56:19

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

#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]