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If a^(2) + b^(2) + c^(3) + ab + bc + ca ...

If `a^(2) + b^(2) + c^(3) + ab + bc + ca le 0` for all, `a, b, c in R`, then the value of the determinant
`|((a + b +2)^(2),a^(2) + b^(2),1),(1,(b +c + 2)^(2),b^(2) + c^(2)),(c^(2) + a^(2),1,(c +a +2)^(2))|`, is equal to

A

65

B

`a^(2)+b^(2)+c^(2)+31`

C

`4(a^(2)+b^(2)+c^(2))`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A
`a+b=0 , b+c = 0, c+a = 0`
`a=b=c=0`
`rArr |(4,0,1),(1,4,0),(0,1,4)|=65`
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