1. Giải các phương trình sau: 

a)\(\sqrt[4]{x-\sqrt{x^2-1}}+\sqrt[]{x+\sqrt{x^2-1}}=2\)

b)\(x^2-x-\sqrt{x^2-x+13}=7\)

c)\(x^2+2\sqrt{x^2-3x+1}=3x+4\)

d)\(2x^2+5\sqrt{x^2+3x+5}=23-6x\)

e)\(\sqrt{x^2+2x}=-2x^2-4x+3\)

f)\(\sqrt{\left(x+1\right)\left(x+2\right)}=x^2+3x+4\)

2. Giải các bất phương trình sau:

1)\(\sqrt{x^2-4x+5}\ge2x^2-8x\)

2)\(2x^2+4x+3\sqrt{3-2x-x^2}>1\)

3)\(\dfrac{\sqrt{-3x+16x-5}}{x-1}\le2\)

4)\(\sqrt{x^2-3x+2}+\sqrt{x^2-4x+3}\ge2\sqrt{x^2-5x+4}\)

5)\(\dfrac{9x^2-4}{\sqrt{5x^2-1}}\le3x+2\)

Giải các hệ phương trình sau

\(1)\left\{{}\begin{matrix}\sqrt{x+1}=\sqrt{2}\left(8y^2+8y+1\right)\\4\left(x^3-8y^3\right)-6\left(x^2+4y^2\right)+3\left(x+2y\right)-1=0\end{matrix}\right.\)

\(2)\left\{{}\begin{matrix}3\sqrt{17x^2-y^2-6x+4}+x=6\sqrt{2x^2+x+y}-3y+2\\\sqrt{3x^2+xy+1}=\sqrt{x+1}\end{matrix}\right.\)

\(3)\left\{{}\begin{matrix}x^3+\left(2-y\right)x^2+\left(2-3y\right)x=5\left(x+1\right)\\3\sqrt{y+1}=3x^2-14x+14\end{matrix}\right.\)

\(4)\left\{{}\begin{matrix}4x^2=\left(\sqrt{x^2+1}+1\right)\left(x^2-y^3+3y-2\right)\\x^2+\left(y+1\right)^2=2\left(1+\dfrac{1-x^2}{y}\right)\end{matrix}\right.\)

\(5)\left\{{}\begin{matrix}7x^3+y^3+3xy\left(x-y\right)-12x^2+6x-1=0\\y^2+7y-17=9x+2\left(x+6\right)\sqrt{5-2y}\end{matrix}\right.\)

\(6)\left\{{}\begin{matrix}2x^2+3=4\left(x^2-2yx^2\right)\sqrt{3-2y}+\dfrac{4x^2+1}{x}\\\left(2x+1\right)\sqrt{2-\sqrt{3-2y}}=\sqrt[3]{2x^2+x^3}+x+2\end{matrix}\right.\)

Giải phương trình bằng phương pháp bất đẳng thức

1, \(\sqrt{x^2-6x+11}+\sqrt{x^2-6x+13}+\sqrt[4]{x^2-4x+5}=3+\sqrt{2}\)

2, \(\sqrt{x-10}+\sqrt{30-x}=x^2-40x+400+2\sqrt{10}\)

3, \(x^2-3x+3,5=\sqrt{\left(x^2-2x+2\right)\left(x^2-4x+5\right)}\)

4, \(\sqrt{5x^3+3x^2+3x-2}=\dfrac{x^2}{2}+3x-\dfrac{1}{2}\)

5, \(2\sqrt{7x^3-11x^2+25x-12}=x^2+6x-1\)

Giải các phương trình sau:
1) \(\sqrt{3x^2+5x+8}-\sqrt{3x^2+5x+1}=1\)
2) \(x^2-2x-12+4\sqrt{\left(4-x\right)\left(2+x\right)}=0\)
3) \(3\sqrt{x}+\dfrac{3}{2\sqrt{x}}=2x+\dfrac{1}{2x}-7\)
4) \(\sqrt{x}-\dfrac{4}{\sqrt{x+2}}+\sqrt{x+2}=0\)
5)\(\left(x-7\right)\sqrt{\dfrac{x+3}{x-7}}=x+4\)
6) \(2\sqrt{x-4}+\sqrt{x-1}=\sqrt{2x-3}+\sqrt{4x-16}\)
7) \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+3}{2}\)
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