If a − b − c 2 b 2 c 2 a b − c − a 2 c 2 a 2 b c − a − b = ( a + b + c ) ( x + a + b + c ) 2 , x  = 0 and a + b + c  = 0 , then x is equal to

Question

If ​ a − b − c 2 b 2 c ​ 2 a b − c − a 2 c ​ 2 a 2 b c − a − b ​ ​ = ( a + b + c ) ( x + a + b + c ) 2 , x  = 0 and a + b + c  = 0 , then x is equal to

TestHub · Accepted Answer

Δ = ​ a − b − c 2 b 2 c ​ 2 a b − c − a 2 c ​ 2 a 2 b c − a − b ​ ​ R 1 ​ → R 1 ​ + R 2 ​ + R Δ = ​ a + b + c 2 b 2 c ​ a + b + c b − c − a 2 c ​ a + b + c 2 b c − a − b ​ ​ = ( a + b + c ) ​ 1 2 b 2 c ​ 1 b − c − a 2 c ​ 1 2 b c − a − b ​ ​ C 1 ​ → C 1 ​ − C y ​ , C 2 ​ → C 2 ​ − C 3 ​ Δ = ( a + b + c ) ​ 0 0 c + a + b ​ 0 − b − c − a c + a + b ​ 1 2 b c − a − b ​ ​ ​ = ( a + b + c ) ( a + b + c ) 2 Hence, x = − 2 ( a + b + c )

Mathematics - Determinant Question with Solution | TestHub

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