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ĐK:\(-2\le x\le2\)
Đặt \(\sqrt{2+x}-2\sqrt{2-x}=t\left(t\ge0\right)\)
\(\Leftrightarrow t^2=10-3x-4\sqrt{4-x^2}\)
\(\Leftrightarrow4\sqrt{4-x^2}=10-3x-t^2\)
PT\(\Leftrightarrow3t+10-3x-t^2=10-3x\)
\(\Leftrightarrow t^2-3t=0\Leftrightarrow\left[{}\begin{matrix}t=0\\t=3\end{matrix}\right.\) (tm) => Giải x
hệ phương trình
1 ,\(\left\{{}\begin{matrix}\frac{2x-3}{2y-5}=\frac{3x+1}{3y-4}\\2\left(x-3\right)-3\left(y+2\right)=-16\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\frac{x}{y}=\frac{3}{2}\\3x-2y=5\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}\frac{x^2-y-6}{x}=x-2\\x+3y=8\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}\frac{x}{y}=\frac{2}{3}\\x+y=10\end{matrix}\right.\)
5, \(\left\{{}\begin{matrix}\frac{y^2+2x-8}{y}=y-3\\x+y=10\end{matrix}\right.\)
6 , \(\left\{{}\begin{matrix}\frac{x+1}{y-1}=5\\3\left(2x-2\right)-4\left(3x+4\right)=5\end{matrix}\right.\)
7, \(\left\{{}\begin{matrix}2x+y=4\\\left|x-2y\right|=3\end{matrix}\right.\)
8 , \(\left\{{}\begin{matrix}\frac{2x}{x+1}+\frac{y}{y+1}=3\\\frac{x}{x+1}-\frac{3y}{y+1}=-1\end{matrix}\right.\)
9 , \(\left\{{}\begin{matrix}y-\left|x\right|=1\\2x-y=1\end{matrix}\right.\)
10 , \(\left\{{}\begin{matrix}\sqrt{x+3y}=\sqrt{3x-1}\\5x-y=9\end{matrix}\right.\)
Giải hệ phương trình:
\(\left\{{}\begin{matrix}y^3-4y^2+4y=\sqrt{x+1}\left(y^2-5y+4+\sqrt{x+1}\right)\\2\sqrt{x^2-3x+3}+6x-7=y^2\left(x-1\right)^2+\left(y^2-1\right)\sqrt{3x-2}\end{matrix}\right.\)
giải hệ phương trình:
\(\left\{{}\begin{matrix}6\sqrt{6x^3+x^2+x-5}=\left(x-\frac{4}{x}+7\right)\left(x^2+\frac{4}{x}\right)\\2\sqrt{3x}+x+5=\left(y+1\right)^2\end{matrix}\right.\)
Giải hpt \(\left\{{}\begin{matrix}\sqrt{y+3x}+\sqrt{2x+7y}=\sqrt{5x-y}+3\sqrt{x}\\x-4-\sqrt{y-2}=\sqrt{x^3-10x^2+33x-34}-\sqrt{y^3-9y^2+24y-16}\end{matrix}\right.\)
giải giúp mik bt này vs mn!
1)\(\left\{{}\begin{matrix}2x^2+y^2+x=3\left(xy+1\right)+2y\\\dfrac{2}{3+\sqrt{2x-y}}+\dfrac{2}{3+\sqrt{4-5x}}=\dfrac{9}{2x-y+9}\end{matrix}\right.\)
2)\(\left\{{}\begin{matrix}\left(x+3y+1\right)\sqrt{2xy+2y}=y\left(3x+4y+3\right)\\\left(\sqrt{x+3}-\sqrt{2y-2}\right)\left(x-3+\sqrt{x^2+x+2y-4}\right)=4\end{matrix}\right.\)
3)\(\left\{{}\begin{matrix}x-\dfrac{1}{x}=y-\dfrac{1}{y}\\2y=x^3+1\end{matrix}\right.\)
4)\(\left\{{}\begin{matrix}\sqrt{2x-3}=\left(y^2+2011\right)\left(5-y\right)+\sqrt{y}\\y\left(y-x+2\right)=3x+3\end{matrix}\right.\)
5)\(\left\{{}\begin{matrix}x^3+2x^2=x^2y+2xy\\2\sqrt{x^2-2y-1}+\sqrt[3]{y^3-14=x-2}\end{matrix}\right.\)
giải hệ pt:
\(\left\{{}\begin{matrix}\left(x-y\right)^2+\frac{4xy}{x+y}=1\\\sqrt{3x+y}-4\sqrt{x+y}=\left(3x+y-6\right)^2-4x\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}x^3+2y^2=x^2y+2xy\\2\sqrt{x^2-2y-1}+\sqrt[3]{y^3-14}=x-2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}2\sqrt{x+y^2+y+3}-3\sqrt{y}=\sqrt{x+2}\\y^3+y^2-3y-5=3x-3\sqrt[3]{x}+2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}\left(x-2\right)\left(2y-1\right)=x^3+20y-28\\2\left(\sqrt{x+2y}+y\right)=x^2+x\end{matrix}\right.\)
Giải hệ phương trình: \(\left\{{}\begin{matrix}\sqrt{x^2+x+1}-\sqrt{y^2-y+1}=\sqrt{x^2+y^2-\frac{1}{2}}\\2x^3y-x^2=\sqrt{x^4+x^2}-2x^3y\sqrt{4y^2+1}\end{matrix}\right.\)
giải hệ phương trình
1, \(\left\{{}\begin{matrix}2x^2+3y=17\\3x^2-2y=6\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\left|x-1\right|+\left|y-1\right|=2\\4\left|x-1\right|+3\left|y-1\right|=7\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}3\sqrt{x-1}+2\sqrt{y}=2\\2\sqrt{x-1}-\sqrt{y}=4\end{matrix}\right.\)
4 , \(\left\{{}\begin{matrix}x+y=2\\\left|2x-3y\right|=1\end{matrix}\right.\)
5 , \(\left\{{}\begin{matrix}2x-y=1\\\left|x-y\right|=\left|2y-1\right|\end{matrix}\right.\)
6,\(\left\{{}\begin{matrix}\left(x-3\right)\left(y+6\right)=xy\\\left(x+2\right)\left(y-2\right)=xy\end{matrix}\right.\)
7 , \(\left\{{}\begin{matrix}\left(x-3\right)\left(2y+5\right)=\left(2x+7\right)\left(y-1\right)\\\left(4x+1\right)\left(3y-6\right)=\left(6x-1\right)\left(2y+3\right)\end{matrix}\right.\)
8 , \(\left\{{}\begin{matrix}4x^2-5\left(y+1\right)=\left(2x-3\right)^2\\3\left(7x+2\right)=5\left(2y-1\right)-3x\end{matrix}\right.\)
