ĐKXĐ: ...
\(\Leftrightarrow2\left(x+1\right)^2=9x\left(\frac{x+1}{\sqrt{x+2}+1}\right)^2\)
TH1: \(\left(x+1\right)^2=0\)
TH2: \(2=\frac{9x}{\left(\sqrt{x+2}+1\right)^2}\)
\(\Leftrightarrow2\left(x+3+2\sqrt{x+2}\right)=9x\)
\(\Leftrightarrow4\sqrt{x+2}=7x-6\) (\(x\ge\frac{6}{7}\))
\(\Leftrightarrow16\left(x+2\right)=\left(7x-6\right)^2\)
\(\Leftrightarrow...\)
Giải phương trình 1, \(x^2+9x+7=\left(2x+1\right)\sqrt{2x^2+4x+5}\)
2, GPT \(\left(2x+7\right)\sqrt{2x+7}=x^2+9x+7\)
3. GHPT \(\left\{{}\begin{matrix}x^2-2y-1=2\sqrt{5y+8}+\sqrt{7x-1}\\\left(x-y\right)\left(x^2+xy+y^2+3\right)=3\left(x^2+y^2\right)+2\end{matrix}\right.\)
Giải hệ \(\left\{{}\begin{matrix}2\left(1+x\sqrt{y}\right)^2=9x\sqrt{y}\\2\left(1+y\sqrt{x}\right)^2=9y\sqrt{x}\end{matrix}\right.\)
Giải PT sau :
\(3x\left(2+\sqrt{9x^2+3}\right)-\left(4x+1\right)\left(1+\sqrt{1+x+x^2}\right)=0\)
Giải hệ phương trình:
1. \(\left\{{}\begin{matrix}x+3=2\sqrt{\left(3y-x\right)\left(y+1\right)}\\\sqrt{3y-2}-\sqrt{\dfrac{x+5}{2}}=xy-2y-2\end{matrix}\right.\)
2. \(\left\{{}\begin{matrix}\sqrt{2y^2-7y+10-x\left(y+3\right)}+\sqrt{y+1}=x+1\\\sqrt{y+1}+\dfrac{3}{x+1}=x+2y\end{matrix}\right.\)
3. \(\left\{{}\begin{matrix}\sqrt{4x-y}-\sqrt{3y-4x}=1\\2\sqrt{3y-4x}+y\left(5x-y\right)=x\left(4x+y\right)-1\end{matrix}\right.\)
4. \(\left\{{}\begin{matrix}9\sqrt{\dfrac{41}{2}\left(x^2+\dfrac{1}{2x+y}\right)}=3+40x\\x^2+5xy+6y=4y^2+9x+9\end{matrix}\right.\)
5. \(\left\{{}\begin{matrix}\sqrt{xy+\left(x-y\right)\left(\sqrt{xy}-2\right)}+\sqrt{x}=y+\sqrt{y}\\\left(x+1\right)\left[y+\sqrt{xy}+x\left(1-x\right)\right]=4\end{matrix}\right.\)
6. \(\left\{{}\begin{matrix}x^4-x^3+3x^2-4y-1=0\\\sqrt{\dfrac{x^2+4y^2}{2}}+\sqrt{\dfrac{x^2+2xy+4y^2}{3}}=x+2y\end{matrix}\right.\)
7. \(\left\{{}\begin{matrix}x^3-12z^2+48z-64=0\\y^3-12x^2+48x-64=0\\z^3-12y^2+48y-64=0\end{matrix}\right.\)
Giải phương trình \(\sqrt{x^3-4x^2+5x-2}-\sqrt{\left(x-2\right)^5}=\left(x-1\right)\sqrt{9x^3-18x^2}\)
Giải các phương trình sau:
a)\(\sqrt{x^2+\frac{9x^2}{\left(x-3\right)^2}}=16\)
b)\(\sqrt{x\left(x-1\right)}+\sqrt{x\left(x-5\right)}=2\sqrt{x^2}\)
giải phương trình
\(2\left(x+1\right)^2=9x\left(\sqrt{x+2-1}\right)^2\)
Giải pt : a) \(8x^2-13x+7=\left(1+\frac{1}{x}\right)\sqrt[3]{3x^2-2}\)
b) \(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=9x-3\)
c) \(2\sqrt{x+1}+6\sqrt{9-x^2}+6\sqrt{\left(x+1\right)\left(9-x^2\right)}=38+10x-2x^2-x^3\)
A)\(\sqrt{4x^2+5x+1}-2\sqrt{x^2-x+1}=9x-3\)
B) \(\left\{{}\begin{matrix}\sqrt{x+y+1}+1=\left(x+y\right)^2+\sqrt{2x+2y}\\x^2-xy=3\end{matrix}\right.\)
