`x - 4 sqrt{x-1} =6`
`<=> sqrt{ 16(x-1) } = x-6`
`<=> sqrt{16x-16} = x-6`
`<=> 16x-16 = (x-6)^2`
`<=> 16x-16 = x^2 - 12x + 36`
`<=> 16x -x^2 +12x = 36 +16`
`<=> -x^2 +28x -52`
`<=> -(x^2 -28x +52) =0`
`<=> x^2 -28x +52=0`
`=> Delta = (-28)^2 - 4*1*52 = 576 > 0`
`=> PT ` có `2` nghiệm riêng biệt
`=>`\(\left\{{}\begin{matrix}x_1=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{-\left(-28\right)+\sqrt{576}}{2\cdot1}\\x_2=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{-\left(-28\right)-\sqrt{576}}{2\cdot1}\end{matrix}\right.\)
`<=>`\(\left\{{}\begin{matrix}x_1=\dfrac{28+24}{2}=26\\x_2=\dfrac{28-24}{2}=2\end{matrix}\right.\)
Mik bổ sung thêm
\(ĐKXĐ:\left\{{}\begin{matrix}\sqrt{x-1}\ge0\\x-6\ge0\end{matrix}\right.\)
`<=>`\(\left\{{}\begin{matrix}x\ge1\left(1\right)\\x\ge6\left(2\right)\end{matrix}\right.\)
Từ `(1);(2)` suy ra : `x>=6`
