Value of X

$\begin{aligned} \sqrt{11x-6} & = \sqrt{4x+5} + \sqrt{x-1} & \small \color{#3D99F6} \text{Squaring both sides.} \\ 11x-6 & = 4x+5 + 2\sqrt{(4x+5)(x-1)} + x-1 \\ 6x - 10 & = 2\sqrt{4x^2+x-5} \\ 3x - 5 & = \sqrt{4x^2+x-5} & \small \color{#3D99F6} \text{Squaring both sides.} \\ 9x^2 - 30x + 25 & = 4x^2+x-5 \\ 5x^2 - 31x + 30 & = 0 \\ (5x-6)(x-5) & = 0 \end{aligned}$

$\implies x = \begin{cases} \frac 65 & \implies \sqrt{11 \times \frac 65-6} = \sqrt{4 \times \frac 65+5} + \sqrt{\frac 65-1} \implies \frac 6{\sqrt 5} {\color{#D61F06}\ne} \frac 7{\sqrt 5} + \frac 1{\sqrt 5} & \small \color{#D61F06} \text{Rejected} \\ \boxed{5} & \implies \sqrt{11 \times 5-6} = \sqrt{4 \times 5+5} + \sqrt{5-1} \implies 7 {\color{#3D99F6} =} 5 + 2 & \small \color{#3D99F6} \text{Accepted} \end{cases}$

First of all square both sides.Left side will be, 11x - 6. Other side will be in formula -. (a+b)^2 Then solving the equation, x = 6/5 and x = 5. Then verify the equation. x = 6/5 won't equal both sides. But x = 5 will equal both sides. Therefore, x = 5