\(a,\)\(T=\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\frac{x+1}{\sqrt{x}}\)

\(=\frac{\sqrt{x}^3-1}{\sqrt{x}\left(\sqrt{x}-1\right)}-\)\(\frac{\sqrt{x}^3+1}{\sqrt{x}\left(\sqrt{x}+1\right)}+\frac{x+1}{\sqrt{x}}\)

\(=\frac{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-1\right)}\)\(-\frac{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}+1\right)}+\frac{x+1}{\sqrt{x}}\)

\(=\frac{x+\sqrt{x}+1-x+\sqrt{x}-1+x+1}{\sqrt{x}}\)

\(=\frac{x+2\sqrt{x}+1}{\sqrt{x}}=\frac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}}\)

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

\(\Rightarrow x^2-2x=2-3x\)

\(\Rightarrow x^2+x-2=0\)

\(\Rightarrow x^2-x+2x-2=0\)

\(\Rightarrow\left(x-1\right)\left(x+2\right)=0\)

\(\Rightarrow\orbr{\begin{cases}x-1=0\\x+2=0\end{cases}\Rightarrow\orbr{\begin{cases}x=1\\x=-2\end{cases}}}\)

Toán Học Team

\(=\frac{1}{2+\sqrt{3}}+\sqrt{3}-1+\sqrt{6+4\sqrt{2}}\)

\(=2-\sqrt{3}+\sqrt{3}-1+\sqrt{\left(2+\sqrt{2}\right)^2}\)

\(=3+\sqrt{2}\)

(1+√2-3)(1+√2+3)=(1+√2)²-9=1+2√2+2+9=12+2√2

SAI ĐỀ BÀI RỒI

4cm2

a) \(x+\sqrt{4x^2-4x+1}=2\)

\(\Leftrightarrow x+\sqrt{\left(2x-1\right)^2}=2\)

\(\Leftrightarrow x+|2x-1|=2\)

\(TH1:x\ge0\)

\(\Leftrightarrow x+2x-1=2\)

\(\Leftrightarrow3x-1=2\)

\(\Leftrightarrow3x=3\)

\(\Leftrightarrow x=1\left(TM\right)\)

\(TH2:x< 0\)

\(\Leftrightarrow x-2x-1=2\)

\(\Leftrightarrow-x-1=2\)

\(\Leftrightarrow-x=3\)

\(\Leftrightarrow x=-3\left(TM\right)\)

Vậy:...

b) \(3x-1-\sqrt{4x^2-12x+9}=0\)

\(\Leftrightarrow3x-1-\sqrt{\left(2x-3\right)^2}=0\)

\(\Leftrightarrow3x-1-|2x-3|=0\)

\(TH1:x\ge0\)

\(\Leftrightarrow3x-1-2x+3=0\)

\(\Leftrightarrow x+2=0\Leftrightarrow x=-2\left(KTM\right)\)

\(TH2:x< 0\)

\(\Leftrightarrow3x-1+2x-3=0\)

\(\Leftrightarrow5x-4=0\Leftrightarrow x=\frac{4}{5}\left(KTM\right)\)

Vậy: pt vô nghiệm

Học Tốt!!!