If |a-b-c&2a&2a 2b&b-c-a&2b 2c&2c&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&2a&2a 2b&b-c-a&2b 2c&2c&c-a-b| = (a + b + c) (x + a + b + c)2, x ≠ 0 and a + b + c ≠ 0, then x is equal to : (A) -(a + b + c) (B) 2(a + b + c) (C) abc (D) -2(a + b + c)

Tardigrade Admin · Accepted Answer

Q. If $∣ ∣ a - b - c 2 b 2 c 2 a b - c - a 2 c 2 a 2 b c - a - b ∣ ∣ = (a + b + c) (x + a + b + c)^{2}, x \neq = 0$ and $a + b + c \neq = 0$ , then $x$ is equal to :

$- (a + b + c)$

$2 (a + b + c)$

$ab c$

$- 2 (a + b + c)$

Q. If ∣∣​a−b−c2b2c​2ab−c−a2c​2a2bc−a−b​∣∣​=(a+b+c)(x+a+b+c)2,x=0 and a+b+c=0, then x is equal to :

−(a+b+c)

2(a+b+c)

abc

−2(a+b+c)

∣∣​a−b−c2b2c​2ab−c−a2c​2a2bc−a−b​∣∣​ R1​→R1​+R2​+R3​ =∣∣​a+b+c2b2c​a+b+cb−c−a2c​a+b+c2bc−a−b​∣∣​ =(a+b+c)∣∣​12b2c​0−(a+b+c)2c​00c−a−b​∣∣​ =(a+b+c)(a+b+c)2 ⇒x=−2(a+b+c)

Q. If $∣ ∣ a - b - c 2 b 2 c 2 a b - c - a 2 c 2 a 2 b c - a - b ∣ ∣ = (a + b + c) (x + a + b + c)^{2}, x \neq = 0$ and $a + b + c \neq = 0$ , then $x$ is equal to :

$- (a + b + c)$

$2 (a + b + c)$

$ab c$

$- 2 (a + b + c)$