Đáp án:
`S={3/2}`
Giải thích các bước giải:
`\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5`
⇔`\sqrt{2x-3+2.\sqrt{2x-3}.1+1}+\sqrt{2x-3+2.\sqrt{2x-3}.4+16}=5`
⇔`\sqrt{(\sqrt{2x-3}+1)^2}+\sqrt{(\sqrt{2x-3}+4)^2}=5`
⇔`|\sqrt{2x-3}+1|+|\sqrt{2x-3}+4|=5`
⇔`\sqrt{2x-3}+1+\sqrt{2x-3}+4=5` `(x>=3/2)`
⇔`2\sqrt{2x-3}=5-4-1`
⇔`2\sqrt{2x-3}=0`
⇔`\sqrt{2x-3}=0`
⇔`2x-3=0`
⇔`2x=3`
⇔`x=3/2` `(tm)`
Vậy `S={3/2}`
