$\sqrt{x-3}+\sqrt{5-x}+\sqrt{2x-7}=2x^2-9x+7$
$⇔\sqrt{x-3}-1+\sqrt{5-x}-1+ \sqrt{2x-7}=2x^2-9x+4 $
$⇔\dfrac{x-3-1}{\sqrt{x-3}+1 }+$$\dfrac{5-x-1}{\sqrt{5-x} +1}+$$\dfrac{2x-7-1}{\sqrt{2x-7}+1}=(x-4)(2x-1)$
$⇔\dfrac{x-4}{\sqrt{x-3}+1}-$ $\dfrac{x-4}{\sqrt{5-x} +1}+$ $\dfrac{2(x-4)}{\sqrt{2x-7}+1}=(x-4)(2x-1)$
$⇔(x-4)[\dfrac{1}{\sqrt{x-3}+1}-\dfrac{1}{\sqrt{5-x} +1}+\dfrac{2}{\sqrt{2x-7}+1} -(2x-1)]=0$
$⇔x=4(vì \dfrac{1}{\sqrt{x-3}+1}-\dfrac{1}{\sqrt{5-x} +1}+\dfrac{2}{\sqrt{2x-7}+1} -(2x-1) \ne 0)$
