Ta có: \(\frac{2x^2-3x+10}{x+2}=\sqrt[3]{\frac{x^2-2x+4}{x+2}}\left(1\right)\)
\(Đkxđ:x>-2\)
\(\left(1\right)\Leftrightarrow\frac{2x^2-3x+10}{1}=3\sqrt{\left(x+2\right)\left(x^2-2x+4\right)}\)
\(\Leftrightarrow\left(2x^2-3x+10\right)^2=9\left(x+2\right)\left(x^2-2x+4\right)\)
\(\Leftrightarrow4x^4+9x^2+100-12x^3+40x^2-60x=9\left(x^3+8\right)\)
\(\Leftrightarrow x=2\left(tm\right)\)
Vậy ..........
Giải phương trình sau:
\(\sqrt{\frac{1-2x}{x}}=\frac{3x+x^2}{x^2+1}\)
\(x^2-3x+1=-\frac{\sqrt{3}}{3}\sqrt{x^4+x^2+1}\)
\(x^2-\sqrt{x^3+x}=6x-1\)
\(3\sqrt{x^2-\frac{1}{4}+\sqrt{x^2+x+\frac{1}{4}}}=\frac{1}{2}\left(2x^3+x^2+2x+1\right)\)
\(x^2+\frac{8x^3}{\sqrt{9-x^2}}=9\)
Giair phương trình
a, \(3\sqrt{\left(x+1\right)\left(x-3\right)}+x^2-2x=7\)
b, \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-16\)
c, \(\left(x^2-4\right)+4\left(x-2\right).\sqrt{\frac{x+2}{x-2}}=3\)
d, \(\frac{9}{x^2}+\frac{2x}{\sqrt{2x^2+9}}=1\)
e, \(3\sqrt{2+x}-6\sqrt{2-x}+4\sqrt{4-x^2}=10-3x\)
Giải phương trình vô tỉ:
a) \(1+\frac{2}{3}\sqrt{x-x^2}=\sqrt{x}+\sqrt{1-x}\)
b) \(\sqrt{2x+3}+\sqrt{x+1}=3x+2\sqrt{2x^2+5x+3}-2\)
c) \(\sqrt{7x+7}+\sqrt{7x-6}+2\sqrt{49x^2+7x-42}=181-4x\)
d) \(\frac{\sqrt{x+4}+\sqrt{x-4}}{2}=x+\sqrt{x^2-16}-6\)
e) \(5\sqrt{x}+\frac{5}{2\sqrt{x}}=2x+\frac{1}{2x}+4\)
g) \(\sqrt{3x-2}+\sqrt{x-1}=4x-9+2\sqrt{3x^2-5x+2}\)
Giải phương trình: \(\frac{x-3x^2}{2}+\sqrt{2x^4-x^3+7x^2-3x+3}=2\)
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 phương trình:
\(a)\sqrt{x^2+2x+4}\ge x-2\\ b)x=\sqrt{x-\frac{1}{x}}+\sqrt{x+\frac{1}{x}}\\ c)\sqrt{x+2+3\sqrt{2x-5}}+\sqrt{x-2\sqrt{2x-5}}\\ d)x+y+z+4=2\sqrt{x-2}+4\sqrt{y-3}+6\sqrt{z-5}\\ e)\sqrt{x}+\sqrt{y-1}+\sqrt{z-2}=\frac{1}{2}\left(x+y+z\right)\)
Giải phương trình, hệ phương trình:
a) \(\frac{\sqrt{x-2013}-1}{x-2013}+\frac{\sqrt{y-2014}-1}{y-2014}+\frac{\sqrt{z-2015}-1}{z-2015}=\frac{3}{4}\)
b) \(\left\{{}\begin{matrix}x^3+1=2y\\y^3+1=2x\end{matrix}\right.\)
c)\(\sqrt{x^2-3x+2}+\sqrt{x-3}=\sqrt{x-2}+\sqrt{x^2+2x-3}\)
d)\(5x-2\sqrt{x}\left(2+y\right)+y^2+1=0\)
giải phương trình ( đặt ẩn phụ )
1) x2-2x+3=2.\(\sqrt{2x^2-4x+3}\)
2) x2+2x.\(\sqrt{x-\frac{1}{x}}\)= 3x+2
3)x4-2x3+x-\(\sqrt{2\left(x^2-x\right)}\)=0
( đặt 2 ẩn phụ )
1) x2+2=2\(\sqrt{x^3+1}\)
2) 3.\(\sqrt{x^3+8}\)=2x2-3x+10
3) \(\sqrt{4x+1}\)-\(\sqrt{3x-2}\)=x+3
Giải phương trình:
a) \(\sqrt{\frac{2x-1}{x+1}}+\sqrt{\frac{x+1}{2x-1}}=2\)
b) \(2\sqrt[3]{\frac{2x-3}{1-x}}+\sqrt[3]{\frac{1-x}{2x-3}}=3\)
c) \(x+\frac{1}{x}+4\left(\sqrt{x}+\frac{1}{\sqrt{x}}\right)+6=0\)
