Question

giải phương trình:

\(\sqrt{3x-2}-\sqrt{5-2x}=-x^2-x+7\)

Answer 1

ĐKXĐ: \(\frac{2}{3}\le x\le\frac{5}{2}\)

\(\Leftrightarrow x^2+x-6+\sqrt{3x-2}-2+1-\sqrt{5-2x}=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+3\right)+\frac{3\left(x-2\right)}{\sqrt{3x-2}+2}+\frac{2\left(x-2\right)}{1+\sqrt{5-2x}}=0\)

\(\Leftrightarrow\left(x-2\right)\left(x+3+\frac{3}{\sqrt{3x-2}+2}+\frac{2}{1+\sqrt{5-2x}}\right)=0\)

\(\Leftrightarrow x-2=0\) (phần ngoặc to luôn dương)

\(\Rightarrow x=2\)