Solve the following equations.\(\begin{vmatrix}x+2&x+6&x-1\\x+6&x-1&x+

1.	Solve the following equations.\(\begin{vmatrix}x+2&x+6&x-1\\x+6&x-1&x+2\\x-1&x+2&x+6\end{vmatrix}\)=0[(x+2, x+6, x-1) (x+6, x-1 x+2) (x-1, x+2, x+6)] =0
Answer» \(\begin{vmatrix}x+2&x+6&x-1\\x+6&x-1&x+2\\x-1&x+2&x+6\end{vmatrix}\) Applying R₂ → R₂ – R₁ and R₃ → R₃ – R₁ , we get \(\begin{vmatrix}x+2&x+6&x-1\\4&-7&3\\-3&-4&7\end{vmatrix}=0\) ∴ (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 – 1) = 0 ∴ 3x + 7 = 0 ∴ x = -7/3

Solve the following equations.\(\begin{vmatrix}x+2&x+6&x-1\\x+6&x-1&x+2\\x-1&x+2&x+6\end{vmatrix}\)=0[(x+2, x+6, x-1) (x+6, x-1 x+2) (x-1, x+2, x+6)] =0

Answer»

\(\begin{vmatrix}x+2&x+6&x-1\\x+6&x-1&x+2\\x-1&x+2&x+6\end{vmatrix}\)

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

\(\begin{vmatrix}x+2&x+6&x-1\\4&-7&3\\-3&-4&7\end{vmatrix}=0\)

∴ (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 – 1) = 0

∴ 3x + 7 = 0

∴ x = -7/3