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 phương trình
a/ \(\sqrt{3x^2-5x+1}-\sqrt{x^2-2}=\sqrt{3\left(x^2-x-1\right)}-\sqrt{x^2-3x+4}\)
b/ \(x^2=\left(x-4\right)\left(1+\sqrt{1+x}\right)^2\)
c/ \(x^2+x-1=\left(x+2\right)\sqrt{x^2-2x+2}\)
d/ \(\sqrt[3]{x+24}+\sqrt{12-x}=6\)
giải các phương trình sau:
a, (x+3) \(\sqrt{2x^2+1}=x^2+1+3\)
b, \(\left(3x+1\right)\sqrt{x^2+3}=3x^2+2x+3\)
c, \(x^2+\sqrt{x^2+11}=31\)
d,\(\left(x+5\right)\left(2-x\right)=3\sqrt{x^2+3x}\)
e, \(\frac{x^2+x+1}{\sqrt{x^2-x+1}}=3\sqrt{x}\)
Giải pt:
a) \(x\left(x-4\right)\sqrt{-x^2+4x}+\left(x-2\right)^2=2\)
b) \(\left(x^2+1\right)^2=5-x\sqrt{2x^2+4}\)
c) \(2x^2+3x-14=2\sqrt[3]{2x^2+3x-10}\)
d) \(6x^2+2x+\sqrt[3]{3x^2+x+4}-10=0\)
e) \(\left(x+4\right)\left(x+1\right)-3\sqrt{x^2+5x+2}=6\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}y^3-4y^2+4y=\sqrt{x+1}\left(y^2-5y+4+\sqrt{x+1}\right)\\2\sqrt{x^2-3x+3}+6x-7=y^2\left(x-1\right)^2+\left(y^2-1\right)\sqrt{3x-2}\end{matrix}\right.\)
giải pt
a) \(\sqrt[3]{x+6}+\sqrt{x-1}=x^2-1\)
b) \(\sqrt[3]{x-9}+2x^2+3x=\sqrt{5x-1}+1\)
c) \(\sqrt{3x+1}-\sqrt{6-x}+3x^2-14x-8=0\)
d) \(\sqrt{x+1}-2\sqrt{4-x}=\frac{5\left(x-3\right)}{\sqrt{2x^2+18}}\)
e) \(x^3+5x^2+6x=\left(x+2\right)\left(\sqrt{2x+2}+\sqrt{5-x}\right)\)
Giải các phương trình sau
a/ \(\sqrt{2x+3}+\sqrt{x+1}=3x+2.\sqrt{\left(2x+3\right)\left(x+1\right)}-16\)
b/ \(\sqrt{x}+\sqrt{9-x}=\sqrt{-x^2+9x+9}\)
c/ \(\sqrt{x+1}+\sqrt{4-x}+\sqrt{\left(x+1\right)\left(4-x\right)}=5\)
Giải pt
a) \(x^2-2x+3\sqrt{x^2-2x-3}=7\)
b) \(\left(x-2\right)^2+2=\sqrt{x^2-4x+12}\)
c) \(x^2+\sqrt{x^2+11}=31\)
d) \(\sqrt{2x^2+4x+1}=1-x\left(x+2\right)\)
e) \(\left(x+1\right)\left(x+4\right)=5\sqrt{x^2+5x+28}\)
Giải phương trình
\(-3x^2+x+3+\left(\sqrt{3x+2}-4\right)\sqrt{3x-2x^2}+\left(x-1\right)\sqrt{3x+2}=0\)