Question

Answer 1

 

ĐKXĐ: \(\left\{{}\begin{matrix}x-3>=0\\5-x>=0\\2x-7>=0\end{matrix}\right.\Leftrightarrow\dfrac{7}{2}< =x< =5\)\(PT\Leftrightarrow\sqrt{x-3}-1+\sqrt{5-x}-1+\sqrt{2x-7}-1=2x^2-\dfrac{29}{4}x-3\)

=>\(\dfrac{x-3-1}{\sqrt{x-3}+1}+\dfrac{5-x-1}{\sqrt{5-x}+1}+\dfrac{2x-7-1}{\sqrt{2x-7}+1}=\dfrac{1}{4}\left(x-4\right)\left(8x+3\right)\)

=>\(\left(x-4\right)\left(\dfrac{1}{\sqrt{x-3}+1}-\dfrac{1}{\sqrt{5-x}+1}+\dfrac{2}{\sqrt{2x-7}+1}-\dfrac{1}{4}\left(8x+3\right)\right)=0\)

=>x-4=0

=>x=4(nhận)