`#Sad`
`\sqrt{10x+1}` `+` `\sqrt{3x-5}` `=` `\sqrt{9x+4}` `+` `\sqrt{2x-2}`
`\text{→Điều kiện:}`
`{(x>=-1/(10)),(x>=5/3),(x>=-4/9),(x>=1):}` `⇔` `x >= 5/3`
`\sqrt{10x+1}` `+` `\sqrt{3x-5}` `=` `\sqrt{9x+4}` `+` `\sqrt{2x-2}`
`⇔` `(\sqrt{3x-5}` `-` `\sqrt{2x-2})` `+` `(\sqrt{10x+1}` `-` `\sqrt{9x+4})` `= 0`
`⇔` `(3x-5-2x+2)/(\sqrt{3x-5}+\sqrt{2x-2})` `+` `(10x+1-9x-4)/(\sqrt{10+1}-\sqrt{9x+4})` `=0`
`⇔` `(x-3)/(\sqrt{3x-5}+\sqrt{2x-2})` `+` `(x-3)/(\sqrt{10+1}-\sqrt{9x+4})` `=0`
`⇔` `(x-3)((1)/(\sqrt{3x-5}+\sqrt{2x-2})` `+` `(1)/(\sqrt{10+1}-\sqrt{9x+4}))` `= 0`
`\text{Vì:}`
`((1)/(\sqrt{3x-5}+\sqrt{2x-2})` `+` `(1)/(\sqrt{10+1}-\sqrt{9x+4}))` `> 0` `AA` `x`
`⇔ x-3 = 0`
`⇔ x = 3` `\text{(thỏa mãn)}`
`\text{Vậy S=}` `{3}`
