AP EAMCET2002MathematicsMatrices

If x^2+y^2+z^2 0, x=c y+b z, y=a z+c x and z=b x+a y , then a^2+b^2+c^2+2 a b c is equal to

Options

A1
B2
Ca+b+c
Da b+b c+c a

Correct answer

A. 1

Step-by-step solution

We have, aligned x-c y-b z & =0 -c x+y-a z & =0 -b x-a y+z & =0 aligned Eliminating x, y, z , we get array rr & | array ccc 1 & -c & -b -c & 1 & -a -b & -a & 1 array |=0 & 1 (1-a^2 )+c(-c-a b)-b(c a+b)=0 & 1-a^2-c^2-a b c-a b c-b^2=0 & a^2+b^2+c^2+2 a b c=1 array

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