1. \(\sqrt{x-3}-\sqrt{x}=\sqrt{2x+1}-\sqrt{3x+4}\)
2. \(5.\sqrt{x-1}-\sqrt{36x-36}+\sqrt{9x-9}=\sqrt{8x-12}\)
3. \(\left(1-4x\right).\sqrt{4x^2+1}=8x^2+2x+1\)

Rút gọn biểu thức:

1. ​\(2y.\sqrt{\frac{7}{y}}\left(y>0\right)\) 
2. \(2y.\sqrt{\frac{-7}{y}}\left(y< 0\right)\)
3. \(x-2-\sqrt{4-4x+x^2}\left(x\le2\right)\)

Giair phương trình:

1. \(\left(x^2+6x+10\right)^2+\left(x+3\right)\left(3x^2+20x+36\right)\)=0
2. \(\frac{4x+2}{\sqrt{x+3}}+x\sqrt{x+8}=\)\(x\left(2x+1\right)+2\sqrt{\frac{x+8}{x+3}}\)

1. x² + 4x = (x + 2 ) .\(\sqrt{x^2-2x-15}\)+39
2. (4 - x ).\(\sqrt{x^3+1}=2x^3+2x+1\)
3. \(x^3+3x+2=\left(x+2\right).\sqrt{x^3+2x+1}\)

1. \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
2. \(\frac{\left(7-x\right)\sqrt{7-x}+\left(x-5\right)\sqrt{x-5}}{\sqrt{7-x}+\sqrt{x-5}}=2\)

vận dụng bđt để giải Pt sau

1. \(\sqrt{2x-1}+\sqrt{19-2x}=\frac{6}{-x^2+10x-24}\)
2. \(\left|x+1\right|+\left|x+2\right|+...+\left|x+2005\right|=2006x\)
3. x²=2x⁸+\(\frac{3}{8}\)
4. \(x+\sqrt{3+\sqrt{x}}=3\)
5. \(8x^2+\sqrt{\frac{1}{x}}=\frac{5}{2}\)

Giải phương trình:

1. \(\frac{1}{\left(x-1\right)^3}+\frac{1}{x^3}+\frac{1}{\left(x+1\right)^3}\)\(=\frac{1}{3x\left(x^2+2\right)}\)
2. \(\left(2-\sqrt{3}\right)^x+\left(7-4\sqrt{3}\right)\left(2+\sqrt{3}\right)^x\)\(=4\left(2-\sqrt{3}\right)\)