Đáp án+Giải thích các bước giải:
`\sqrt{x-1}+\sqrt{2x-1}=5(x≥1)`
`⇔x-1+2\sqrt{(x-1)(2x-1)}+2x-1=25`
`⇔3x-2+2\sqrt{2x^2-3x+1}=25`
`⇔2\sqrt{2x^2-3x+1}=27-3x(x≤9)`
`⇔4(2x^2-3x+1)=729-162x+9x^2`
`⇔8x^2-12x+4=729-162x+9x^2`
`⇔x^2-150x+725=0`
`⇔x^2-145x-5x+725=0`
`⇔x(x-145)-5(x-145)=0`
`⇔(x-5)(x-145)=0`
$⇔\left[\begin{matrix}x-5=0\\x-145=0\end{matrix}\right.$
$⇔\left[\begin{matrix}x=5(tm)\\x=145(L)\end{matrix}\right.$
Vậy `S={5}`
