Đáp án:
Giải thích các bước giải:
`\sqrt{x-1}+\sqrt{x-2}=\sqrt{3x-1}`
`ĐK: x \ge 2`
`⇔ x-1+x-2+2\sqrt{(x-1)(x-2)}=3x-1`
`⇔ 2\sqrt{(x-1)(x-2)}=x+2`
`⇔ 4(x-1)(x-2)=x^2+4x+4`
`⇔ 4(x^2-3x+2)=x^2+4x+4`
`⇔ 4x^2-12x+8-x^2-4x-4=0`
`⇔ 3x^2-16x+4=0`
`⇔` \(\left[ \begin{array}{l}x=\dfrac{8+2\sqrt{13}}{3}\ (TM)\\x=\dfrac{8-2\sqrt{13}}{3}\ (L)\end{array}\right.\)
Vậy \(S={\dfrac{8+2\sqrt{13}}{3}}\)
