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Question

If x2+y2+z20, and given x=cy+ bz, y=az+ cx, and z=bx+ ay, then the value of a2+b2+c2+2abc=

A
2
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B
a+b+c
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C
1
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D
ab+bc+ ca
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Solution

The correct option is C 1
xcybz=0
yazcx=0
zbxcy=0
Δ=∣ ∣1cbc1aba1∣ ∣=(1a2)+c(cab)b(ac+b)
Δ=1a2c2abcabcb2
Now, Δ=0 ( infinite solution of this equation)
a2+b2+c2+2abc=1

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