Bài 1:
1. \(\sqrt{x-5}\)+ \(\sqrt{x}\)=\(\sqrt{5}\)
2.\(\frac{x^2}{\sqrt{3x-2}}\)- \(\sqrt{3x-2}\)=1-x
3.\(\sqrt{x+2\sqrt{x-1}}\) + \(\sqrt{x-2\sqrt{x-1}}\)=\(\frac{x+3}{2}\)
4. \(\sqrt{x-1}\)+\(\sqrt{3x-2}\)= 4x-9+2\(\sqrt{3x^2-5x+2}\)
5. \(\sqrt{x+\sqrt{2x-1}}\)+ \(\sqrt{x-\sqrt{2x-1}}\)=\(\sqrt{2}\)
6. x-2\(\sqrt{x-1}\) - (x - 1)\(\sqrt{x}\) + \(\sqrt{x^2-x}\)=0
7. \(\sqrt{x\left(x-1\right)}\) +\(\sqrt{x\left(x+2\right)}\)= 2\(\sqrt{x^2}\)
1. \(x=5\)
2. \(x=1\)
3. \(x=1\)
4. \(x=2\)
5. \(x=0,73\)
6. \(x=2\)
7. \(x=0\)
\(1,\sqrt{x-5}-\sqrt{5}+\sqrt{x}=0\)
\(\Leftrightarrow\sqrt{x-5}+\frac{x-5}{\sqrt{x}+\sqrt{5}}=0\)
\(\Leftrightarrow\sqrt{x-5}\left(1+\frac{\sqrt{x-5}}{\sqrt{x}+\sqrt{5}}\right)=0\)
do \(\left(1+\frac{\sqrt{x-5}}{\sqrt{x}+\sqrt{5}}\right)>0\)\(\Rightarrow x=5\)
\(2,\frac{1}{\sqrt{3x-2}}\left(x^2-3x+2\right)+x-1=0\)
\(\Leftrightarrow\left(x-1\right)\left(1+\frac{x+2}{\sqrt{3x-2}}\right)=0\)
\(\Rightarrow x=1\)
3 \(\sqrt{x-1+2\sqrt{x-1}+1}+\sqrt{x-1-2\sqrt{x-1}+1}=\frac{x+3}{2}\)
\(\left|\sqrt{x-1}+1\right|+\left|\sqrt{x-1}-1\right|=\frac{x+3}{2}\)
đến đây bạn giải nốt nhá
4.\(\sqrt{x-1}-1+\sqrt{3x-2}-2-4x+8-2\left(\sqrt{3x^2-5x+2}-2\right)=0\)
\(\frac{x-2}{\sqrt{x-1}+1}+\frac{3\left(x-2\right)}{\sqrt{3x-2}+2}-4\left(x-2\right)-\frac{2\left(x-2\right)\left(3x+1\right)}{\sqrt{3x^2-5x+2}+2}=0\)
\(\Leftrightarrow\left(x-2\right)\left(\frac{1}{\sqrt{x-1}+1}+\frac{3}{\sqrt{3x-2}+2}-4-\frac{2\left(3x+1\right)}{\sqrt{\left(3x-2\right)\left(x-1\right)}+2}\right)=0\)
\(\Rightarrow x=2\)
\(\sqrt{x+\sqrt{2x-1}}+\sqrt{x-\sqrt{2x-1}}=\sqrt{2}\)
\(\Leftrightarrow2x+2\sqrt{x^2-2x+1}=2\)
\(\Leftrightarrow2x+2\left(x-1\right)=2\)
\(\Leftrightarrow4x=4\Rightarrow x=1\)
\(x-1-2\sqrt{x-1}+1-\left(x-1\right)\sqrt{x}+\sqrt{x}\sqrt{x-1}=0\)
\(\Leftrightarrow\left(\sqrt{x-1}-1\right)^2-\sqrt{x\left(x-1\right)}\left(\sqrt{x-1}-1\right)=0\)
\(\Leftrightarrow\left(\sqrt{x-1}-1\right)\left(\sqrt{x-1}-1-\sqrt{x\left(x-1\right)}\right)=0\)
Bạn giải nốt nhá
