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Question

If x+y+z=0 then what is the value of
1x2+y2z2+1y2+z2x2+1z2+x2y2

A
1x2+y2+z2
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B
1
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C
1
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D
0
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Solution

The correct option is D 0
x+y+z=0x+y=z
On squaring, we get
(x+y)2=(z)2
x2+y2z2=2xy
Similarly,
y2+z2x2=2yz
z2+x2y2=2xz
1x2+y2z2+1y2+z2x2+1z2+x2y2
= 12xy+12yz+12zx=12(z+x+yxyz)=0

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