Let a , b , c be any real numbers. Suppose that there are real numbers x , y , z not all zero such that x = cy + b z , y = a z + c x and z = b x + a y . Then a 2 + b 2 + c 2 + 2 ab c is equal to

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The system of equations x − cy − b z = 0 , c x − y + a z = 0 and b x + a y − z = 0 have non-trivial solution if ​ 1 c b ​ − c − 1 a ​ − b a − 1 ​ ​ = 0 ⇒ 1 ( 1 − a 2 ) + c ( − c − ab ) − b ( c a + b ) = 0 ⇒ a 2 + b 2 + c 2 + 2 ab c = 1 .

Mathematics - Determinant Question with Solution | TestHub

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