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Let a,b,c be any real numbers. Suppose that there are real numbersx,y,z not all zero such that x=cy+bz, y=az+cx, z=bx+ay. Then find the value of a 2 +b 2 +c 2 +2abc.. Explain the step in which the determinant is equatwed to some value.

Let a,b,c be any real numbers. Suppose that there are real numbersx,y,z not all zero such that x=cy+bz, y=az+cx, z=bx+ay. Then find the value of a2+b2+c2+2abc..
Explain the step in which  the determinant is equatwed to some value. 

Grade:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
8 years ago
Hello student,
The system of equations x – cy – bz = 0, cx – y + az = 0 and bx + ay – z = 0 have non-trivial solution if
\begin{vmatrix} 1 &-c &-b \\ c&-1 &a \\ b& a &-1 \end{vmatrix}=0
1(1-a2)+c(-c-ab)-b(ca+b)=0
Soa2+b2+c2+2abc=1
Thanks and Regards
Shaik Aasif
askIITians faculty

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