ĐKXĐ: \(x\ge0\)
\(pt\Leftrightarrow x+1=1+x\sqrt{x}+3x+3\sqrt{x}\)
\(\Leftrightarrow x\sqrt{x}+2x+3\sqrt{x}=0\)
\(\Leftrightarrow\sqrt{x}\left(x+2\sqrt{x}+3\right)=0\)
\(\Leftrightarrow\sqrt{x}\left[\left(\sqrt{x}+1\right)^2+2\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x}=0\\\left(\sqrt{x}+1\right)^2=-2\left(vn\right)\end{matrix}\right.\)
\(\Leftrightarrow x=0\left(tm\right)\)
Giải PT: \(\sqrt[3]{x+2}+\sqrt[3]{x+1}=\sqrt[3]{2x^2}+\sqrt[3]{2x^2+1}\)
giải pt \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3x^2-3x+3}-\sqrt{x^2-3x+4}\)
Giải pt :
a) \(x^2+3x\sqrt[3]{3x+3}-12+\frac{1}{\sqrt{x}}=\frac{\sqrt{x}+8}{x}\)
b) \(\sqrt{\left(x-1\right)\left(3-x\right)}+\sqrt{x+2}=\sqrt{x-1}+\sqrt{3-x}+\frac{x}{2}\)
Giải pt sau
a) \(\sqrt{x^2-2x+5}=x^2-2x-1\)
b)\(\sqrt{4x^2+9x+5}=\sqrt{x^2-1}+\sqrt{2x^2+x-1}\)
Giải pt
\(\sqrt[3]{x^2-1}+x=\sqrt[3]{x^2-x}\)
giải PT
\(\left(\sqrt{x+3}-\sqrt{x+1}\right)\left(x^2+\sqrt{x^2+4x+3}\right)=2x\)
Giải PT: \(\sqrt[3]{x^2-x-1}+x^2-2=\sqrt[3]{2x-3}+3x\)
Giải PT: \(\sqrt{x+1}-2\sqrt{4-x}=\frac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
Giải PT: \(\sqrt{3x-2}-\sqrt{x+1}=2x^2-x-3\)
Giải pt \(\sqrt[3]{x+1}\)+\(\sqrt[3]{x+2}\)+\(\sqrt[3]{x+3}\)=0
