Question

If `[(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)]` = 0, then find values of x.

Answer 1

We have, `|(4 - x, 4 + x, 4 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0

[Applying R₁ → R₁ + R₂ + R₃]

⇒ `|(12 + x, 12 + x, 12 + x),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0

[Taking (12 + x) common from R₁]

⇒ `(12 + x)|(1, 1, 1),(4 + x, 4 - x, 4 + x),(4 + x, 4 + x, 4 - x)|` = 0

[Applying C₁ → C₁ – C₂ and C₂ → C₂ – C₃]

⇒ `(12 + x)|(0, 0, 1),(0, -2x, 4 + x),(2x, 2x, 4 - x)|` = 0

⇒ `(12 + x)(0 - (-2x)(2x)]` = 0

⇒ `(12 + x)(4x^2)` = 0

∴ x = –12, 0