The determinant |x2 (y+z)2 y z y2 (z+x)2 z x z2 (x+y)2 x y| is divisible by:

Question

The determinant |x2 (y+z)2 y z y2 (z+x)2 z x z2 (x+y)2 x y| is divisible by: (A)  x2+y2+z2 (B)  x - y (C) x-y-z (D) x+y+z

Tardigrade Admin · Accepted Answer

Let Δ=|x2 (y+z)2 y z y2 (z+x)2 z x z2 (x+y)2 x y| C 2 arrow C 2-2 C 3 Δ=|x2 y2+z2 y z y2 z2+x2 z x z2 x2+y2 x y| Δ=(x2+y2+z2)(x-y)(y-z)(z-x)(x+y+z)

Q. The determinant $∣ ∣ x^{2} y^{2} z^{2} (y + z)^{2} (z + x)^{2} (x + y)^{2} yz z x x y ∣ ∣$ is divisible by: