ĐK: \(x\ge-1\)
\(\frac{pt\Leftrightarrow\sqrt{x+1}\sqrt{x^2-x+1}}{\sqrt{x+3}}+\sqrt{x+1}=\sqrt{x^2-x+1}+\sqrt{x+3}\)
\(\Leftrightarrow\frac{\sqrt{x+1}}{\sqrt{x+3}}\left(\sqrt{x^2-x+1}+\sqrt{x+3}\right)=\sqrt{x^2-x+1}+\sqrt{x+3}\)
\(\Leftrightarrow\frac{\sqrt{x+1}}{\sqrt{x+3}}=1\text{ (do }\sqrt{x^2-x+1}>0\text{)}\)
\(\Leftrightarrow...\)
giai p.t : \(x\sqrt{x^2-x+1}+4\sqrt{3x+1}=x^2+x+3\)
giai p.t : \(\sqrt[3]{1-x}+\sqrt[3]{1+x}=1\)
giai p.t \(\frac{36}{\sqrt{x-2}}+\frac{4}{\sqrt{y-1}}=28-4\sqrt{x-2}-\sqrt{y-1}\)
giai phuong trinh
\(\frac{1}{\sqrt{x}+\sqrt{x+1}}+\frac{1}{\sqrt{x+1}+\sqrt{x+2}}+\frac{1}{\sqrt{x+2}+\sqrt{x+3}}=1\)
giai p.t :\(\sqrt{x}+2\sqrt{x+3}=x+4\)
Giai các phương trình
1)\(\frac{2+\sqrt{x}}{\sqrt{2}+\sqrt{2+\sqrt{x}}}+\frac{2-\sqrt{x}}{\sqrt{2}-\sqrt{2-\sqrt{x}}}=\sqrt{2}\)
2)\(\frac{\sqrt[3]{7-x}-\sqrt[3]{x-5}}{\sqrt[3]{7-x}+\sqrt[3]{x+5}}=6-x\)
giai p.t : \(\frac{1}{x}+\frac{1}{\sqrt{2-x^2}}=2\)
giai p.t : \(\sqrt{x+1}-\sqrt{x-7}=\sqrt{12-x}\)
giai p.t :\(\sqrt{2x^2+x+6}+\sqrt{x^2+x+2}=x+\frac{4}{x}\)
