Giải phương trình sau:
\(\sqrt{\frac{1-2x}{x}}=\frac{3x+x^2}{x^2+1}\)
\(x^2-3x+1=-\frac{\sqrt{3}}{3}\sqrt{x^4+x^2+1}\)
\(x^2-\sqrt{x^3+x}=6x-1\)
\(3\sqrt{x^2-\frac{1}{4}+\sqrt{x^2+x+\frac{1}{4}}}=\frac{1}{2}\left(2x^3+x^2+2x+1\right)\)
\(x^2+\frac{8x^3}{\sqrt{9-x^2}}=9\)
gpt : a) \(\frac{5x}{\sqrt{4-x^2}}+\frac{8}{x^2}+\frac{2x}{4-x^2}+\frac{5\sqrt{4-x^2}}{x}+4=0\)
b) \(\frac{2x}{\sqrt{8x^2+25}}+\frac{125}{x^2}-14=0\)
c) \(\left(x^3-3x+2\right)\sqrt{3x-2}-2x^3+6x^2-4x=0\)
d) \(\sqrt{x^2-x+6}+\frac{4}{x-1}=x^2+x\)
Giải phương trình:
\(\left\{{}\begin{matrix}\frac{2x+7}{x+2}+\frac{2y}{y-1}=9\\\frac{2x+2}{x+2}+\frac{3y+2}{y-1}=8\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}2y\left(4y^2+3x^2\right)=x^4\left(x^2+3\right)\\2012^x\left(\sqrt{2y-2x+5}-x+1\right)=4024\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3-2x^2y-15x=6y\left(2x-5-4y\right)\\\frac{x^2}{8y}+\frac{2x}{3}=\sqrt{\frac{x^3}{3y}+\frac{x^2}{4}}-\frac{y}{2}\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}8\left(x^2+y^2\right)+4xy+\frac{5}{\left(x+y\right)^2}=13\\2x+\frac{1}{x+y}=1\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}\frac{x^2}{y^2+2y+1}+\frac{y^2}{x^2+2x+1}=\frac{8}{9}\\5xy-4x-4y=4\end{matrix}\right.\)
giải các phương trình sau
1) 15.\(\sqrt{x^3-1}\)=4x2+8
2) \(\sqrt{2x-3}\)+6=2x+\(\sqrt{x}\)
3) \(\sqrt{x-\frac{1}{x}}\)+\(\frac{4}{x}\)=x+\(\sqrt{2x-\frac{5}{x}}\)
4)\(\sqrt{5x-1}\)-\(\sqrt{x+2}\)=\(\frac{4x-3}{5}\)
5) \(\sqrt{2x-\frac{3}{x}}\)-1=\(\frac{3}{2x}\)-\(\sqrt{\frac{6}{x}-2x}\)
Giải phương trình
\(\frac{1}{x^2-2x+2}+\frac{2}{x^2-2x+3}=\frac{6}{x^2-2x+4}\)
giải phương trình:
\(\frac{2x^2-3x+10}{x+2}=3\sqrt{\frac{x^2-2x+4}{x+2}}\)
Giải PT:
\(8^x+27^{\frac{1}{x}}+2^{x+1}\cdot3^{\frac{x+1}{x}}+2^x\cdot3^{\frac{2x+1}{x}}=125\)