Question

giải phương trình

\(\sqrt{x-3}+\sqrt{5-x}-2x^2+7x+2=0\)

Answer 1

ĐKXĐ: \(3\le x\le5\)

\(2x^2-7x-2-\sqrt{x-3}-\sqrt{5-x}=0\)

\(\Leftrightarrow2x^2-7x-4+1-\sqrt{x-3}+1-\sqrt{5-x}=0\)

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

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

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

\(\Leftrightarrow x-4=0\) (ngoặc to luôn dương)

\(\Leftrightarrow x=4\)