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Let a, b, c be any real numbers. Suppo...

Let a, b, c be any real numbers. Suppose that there are real numbers x, y, z not all zero such that `x""=""c y""+""b z ,""y""=""a z""+""c x""a n d""z""=""b x""+""a y` . Then `a^2+""b^2+""c^2+""2a b c` is equal to

A

1

B

2

C

-1

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
Given system of equations is `x-cy-bz=0`
`cx-y+az=0` and `bx+ay-z=0`
For non zero solution `|(1,-c,-b),(c,-1,a),(b,a,-1)|=0`
`implies 1(1-a^(2))+c(-c-ab)-b(ac+b)=0`
`:.a^(2)+b^(2)+c^(2)+2abc=1`
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