Giải các bất phương trình, hệ phương trình
a) \(\dfrac{x^2-4x+3}{2x-3}\ge x-1\)
b) \(3x^2-\left|4x^2+x-5\right|>3\)
c)\(4x-\left|2x^2-8x-15\right|\le-1\)
d)\(x+3-\sqrt{21-4x-x^2}\ge0\)
e)\(\left\{{}\begin{matrix}x\left(x+5\right)< 4x+2\\\left(2x-1\right)\left(x+3\right)\ge4x\end{matrix}\right.\)
f)\(\dfrac{1}{x^2-5x+4}\le\dfrac{1}{x^2-7x+10}\)
Giải các bất phương trình sau:
1) \(x^3+\left(3x^2-4x-4\right)\sqrt{x+1}\le0\)
2) \(\sqrt{2x^2-6x+8}-\sqrt{x}\le x-2\)
3) \(4\left(x+1\right)^2< \left(2x+10\right)\left(1-\sqrt{3+2x}\right)\)
4) \(4\sqrt{x+1}+2\sqrt{2x+3}\le\left(x-1\right)\left(x^2-2\right)\)
Giải các bất phương trình, hệ phương trình
a) \(\dfrac{x^2\left(3x-2\right)\left(x^2-1\right)}{\left(-x^2+2x-3\right)\left(2-x\right)^2}\ge0\)
b) \(\dfrac{x-5}{x-1}>2\)
c) \(2x-\sqrt{x^2-5x-14}< 1\)
d) \(x+\sqrt{x^2-4x-5}< 4\)
e) \(\left\{{}\begin{matrix}\left(4-x\right)\left(x^2-2x-3\right)< 0\\x^2\ge\left(x^2-x-3\right)^2\end{matrix}\right.\)
Giải bpt:
a,\(\frac{\sqrt{x^2-x+4}-2x-3}{x-2}>3\)
b, \(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x+2\right)}\le\sqrt{x\left(4x+1\right)}\)
Giải pt, bất pt
a) \(\left(\sqrt{x+3}-\sqrt{x+1}\right)\left(x^2+\sqrt{x^2+4x+3}=2x\right)\)
b) \(\left(x^2-3x+2\right)\left(x^2-12x+32\right)\le4x^2\)
c) \(2\sqrt{3x+7}-5\sqrt[3]{x-6}=4\)
giải các bất phương trình sau:\(\frac{2x-5}{\left|x-3\right|}+1>0\)
\(\frac{\left|x-2\right|}{x^2-5x+6}>=3\)
\(\sqrt{2x+\sqrt{6x^2+1}}>x+1\)
\(\sqrt{x+3}-\sqrt{7-x}>\sqrt{2x-8}\)
\(\sqrt{2-x}>\sqrt{7-x}-\sqrt{-3-2x}\)
\(\sqrt{2x+3}+\sqrt{x+2}\le1\)
\(\left(x+5\right)\left(x-2\right)+3\sqrt{x\left(x+3\right)}>0\)
giải các bất phương trình sau :
a) \(\left|x^2-2x-3\right|\le3x-3\)
b)\(\frac{2x-4}{\sqrt{x^2-3x-10}}>1\)
c)\(\sqrt{x+3}-\sqrt{7-x}>\sqrt{2x-8}\)
d)\(\left(2x-5\right)\sqrt{2x^2-5x+2}\le0\)
e)\(\left(x+1\right)\left(x+4\right)< 5\sqrt{x^2+5x+28}\)
f)\(\sqrt{3x^2+5x+7}-\sqrt{3x^2+5x+2}\ge1\)
giải hệ phương trình
a) \(\left\{{}\begin{matrix}\sqrt{2x^2+2y^2}+\sqrt{\frac{4}{3}\left(x^2+xy+y^2\right)}=2\left(x+y\right)\\\sqrt{3x+1}+\sqrt{5x+4}=3xy-y+3\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}\sqrt{5x^2+2xy+2y^2}+\sqrt{2x^2+2xy+5y^2}=3\left(x+y\right)\\\sqrt{x+2y+1}+2\sqrt[3]{12x+7y+8}=2xy+x+5\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}x^2+xy+x+3=0\\\left(x+1\right)^2+3\left(y+1\right)+2\left(xy-\sqrt{x^2y+2y}\right)=0\end{matrix}\right.\)
Bài 2 : Giải các phương trình sau
1 , \(x\left(x+5\right)=2\sqrt[3]{x^2+5x-2}-2\)
2 , \(\sqrt[3]{x+5}+\sqrt[3]{x+6}=\sqrt[3]{2x+11}\)
3 , \(\sqrt[4]{x-\sqrt{x^2-1}}+\sqrt{x+\sqrt{x^2-1}}=2\)
4 , \(x^2-2x-8=4\sqrt{\left(4-x\right)\left(x+2\right)}\)
5 , \(x^2+5x+2+2\sqrt{x^2+5x+10}=0\)
6 , \(\sqrt{2x^2+3x-5}=x+1\)
7 , \(\left(x-1\right)\left(x-3\right)+3\sqrt{x^2-4x+5}-2=0\)
