Đặt \(\sqrt[3]{x^2+5x-2}=t\Rightarrow x^2+5x=t^3+2\)
Pt trở thành:
\(2t=t^3+4\Leftrightarrow t^3-2t+4=0\)
\(\Leftrightarrow\left(t+2\right)\left(t^2-2t+2\right)=0\)
\(\Leftrightarrow t=-2\Rightarrow x^2+5x-2=-8\)
\(\Leftrightarrow x^2+5x+6=0\)
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 , \(\left(x-1\right)\left(x-3\right)+3\sqrt{x^2-4x+5}-2=0\)
Giai các bất phương trình sau đây :
a/ \(\sqrt{\left(x-3\right)\left(8-x\right)}+26>-x^2+11x\)
b/ \(\left(x+5\right)\left(x-2\right)+3\sqrt{x\left(x+3\right)}>0\)
c/ \(\left(x+1\right)\left(x+4\right)< 5\sqrt{x^2+5x+28}\)
d/ \(\sqrt{3x^2+5x+7}-\sqrt{3x^2+5x+2}\ge1\)
HELP ME !!!!!!
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)\(\left\{{}\begin{matrix}x^2+xy+x+3=0\\\left(x+1\right)^2+3\left(y+1\right)+2\left(xy-\sqrt{x^2y+2y}\right)=0\end{matrix}\right.\)
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 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 các bất phương trình sau:\(\frac{2x-5}{\left|x-3\right|}+1>0\)
\(\frac{\left|x-2\right|}{x^2-5x+6}>=3\)
\(\sqrt{2x+\sqrt{6x^2+1}}>x+1\)
\(\sqrt{x+3}-\sqrt{7-x}>\sqrt{2x-8}\)
\(\sqrt{2-x}>\sqrt{7-x}-\sqrt{-3-2x}\)
\(\sqrt{2x+3}+\sqrt{x+2}\le1\)
\(\left(x+5\right)\left(x-2\right)+3\sqrt{x\left(x+3\right)}>0\)
giúp mình giải bpt vs
\(\dfrac{\left|2x-1\right|-x}{2x}>1;\dfrac{2-\left|x-2\right|}{x^2-1}\ge0;\dfrac{\sqrt{x+4}-2}{4-9x^2}\le0;\dfrac{x^2-2x-3}{\sqrt[3]{3x-1}+\sqrt[3]{4-5x}}\ge0;\)\(3x^2-10x+3\ge0;\left(\sqrt{2}-x\right)\left(x^2-2\right)\left(2x-4\right)< 0;\dfrac{1}{x+9}-\dfrac{1}{x}>\dfrac{1}{2};\dfrac{2}{1-2x}\le\dfrac{3}{x+1}\)
Bài 1 : giải các phương trình sau
1 , \(\left(x^2-6x\right)\sqrt{17-x^2}=x^2-6x\)
2 , \(\left(x^2+5x+4\right)\sqrt{x+3}=0\)
3, \(\sqrt{3x}+\sqrt{2x-2}=\sqrt{1-x}+2\)
4, \(\left(x^2-4x+3\right)\sqrt{x-2}=0\)
5 , \(\sqrt{x^2+3x-2}=\sqrt{1+x}\)
6 , \(\left(\sqrt{x-4}-1\right)\left(x^2-7x+6\right)=0\)
7, \(\sqrt{2x^2-8x+4}=x-2\)
8 , \(\sqrt{3x+7}-\sqrt{x+1}=2\)
Giải bất phương trình: \(\left(x+1\right)\left(4-x\right)< 5\sqrt{x^2+5x+28}\)
