Đáp án:
`S={{19+\sqrt{73}}/8;{23-\sqrt{97}}/8}`
Giải thích các bước giải:
`\qquad 4x^2-21x+22+\sqrt{3x-2}=0` `(x\ge 2/ 3)`
`<=>4x^2-18x+{81}/4-(3x -2 -\sqrt{3x-2}+1/ 4)=0`
`<=>(2x-9/ 2)^2=(\sqrt{3x-2}-1/ 2)^2`
`<=>`$\left[\begin{array}{l}2x-\dfrac{9}{2}=\sqrt{3x-2}-\dfrac{1}{2}\\2x-\dfrac{9}{2}=-\sqrt{3x-2}+\dfrac{1}{2}\end{array}\right.$
`<=>`$\left[\begin{array}{l}\sqrt{3x-2}=2x-4\ (x\ge 2)\\\sqrt{3x-2}=-2x+5\ (\dfrac{2}{3}\le x\le \dfrac{5}{2})\end{array}\right.$
`<=>`$\left[\begin{array}{l}3x-2=4x^2-16x+16\ (x\ge 2)\\3x-2=4x^2-20x+25\ (\dfrac{2}{3}\le x\le \dfrac{5}{2})\end{array}\right.$
`<=>`$\left[\begin{array}{l}4x^2-19x+18=0\ (x\ge 2)\\4x^2-23x+27=0\ (\dfrac{2}{3}\le x\le \dfrac{5}{2})\end{array}\right.$
`<=>`$\left[\begin{array}{l}x=\dfrac{19-\sqrt{73}}{8}(loại)\\x=\dfrac{19+\sqrt{73}}{8}(TM)\\x=\dfrac{23-\sqrt{97}}{8}(T M)\\x=\dfrac{23+\sqrt{97}}{8}\ (loại)\\\end{array}\right.$
Vậy `S={{19+\sqrt{73}}/8;{23-\sqrt{97}}/8}`
