Question

giải phương trình \(\sqrt{x+1}+\sqrt{x-2}-\sqrt{2x+3}+\sqrt{5x+1}=4\)

Answer 1

Điều kiện: \(x\ge2\)

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

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

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

\(\Leftrightarrow x=3\)

PS: Phần trong ngoặc tự chứng minh nha.