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

By R₂ – R₁ and R₃ – R₁, we get,

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

By C₂ – C₁ and C₃ – C₁, we get,

`|(x + 2, 4, -3),(4, -11, -1),(-3, -1, 10)|` = 0

∴ (x + 2)( –110 – 1) – 4 (40 – 3) – 3 ( –4 – 33) = 0

∴ (x + 2)( – 111) – 4 (37) – 3 ( – 37) = 0

∴ 37[ –3(x + 2) – 4 – 3( – 1)] = 0

∴ – 3 (x + 2) – 4 + 3 = 0

∴ – 3x – 6 – 1 = 0

∴ – 3x = 7

∴ x = `-7/3`.