Question

Solve the following equation: `|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` =  0

Answer 1

`|(x + 2, x + 6, x - 1),(x + 6, x - 1,x + 2),(x - 1, x + 2, x + 6)|` =  0

Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁, we get

`|(x + 2, x + 6, x - 1),(4, -7, 3),(-3, -4, 7)|` = 0

∴ (x + 2)( – 49 + 12) – (x + 6)(28 + 9) + (x – 1) ( – 16 – 21) = 0
∴ (x + 2) ( – 37) – (x +  6) (37) + (x – 1) (– 37) = 0
∴ – 37(x + 2 + x + 6 x + x – 1) = 0
∴ 3x + 7 = 0

 ∴ x = `(-7)/3`