Question

Solve the following equation : `|(x, 2, 2),(2, x, 2),(2, 2, x)| = 0`

Answer 1

`|(x, 2, 2),(2, x, 2),(2, 2, x)| = 0`

∴ `x|(x, 2),(2, x)| - 2|(2, 2),(2, x)| + 2|(2, x),(2, 2)|` = 0

∴ x(x² – 4) –2(2x – 4) + 2(4 – 2x) = 0
∴ x(x² – 4) – 2(2x – 4) –2(2x – 4) = 0
∴ x(x + 2)(x – 2) – 4(2x – 4) = 0
∴ x(x + 2)(x – 2) – 8(x – 2) = 0
∴ (x – 2)[x(x + 2) – 8] = 0
∴ (x – 2)(x² + 2x – 8) = 0
∴ (x – 2)(x² + 4x – 2x –8) = 0
∴ (x – 2)(x + 4)(x – 2) = 0
∴ (x – 2)²(x + 4) = 0
∴ (x – 2)² = 0 or x + 4 = 0
∴ x – 2 = 0 or x = – 4
∴ x = 2 or x = – 4