Violympic toán 9
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giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{x-2}+\sqrt{y-3}=3\\2\sqrt{x-2}-3\sqrt{y-3}=-4\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{3x}{x+1}+\dfrac{2}{y+4}=4\\\dfrac{2x}{x+1}-\dfrac{5}{y+4}=4\end{matrix}\right.\)
Giải hệ phương trình:
a, \(\left\{{}\begin{matrix}\sqrt{2x+3}+\sqrt{4-y}=4\\\sqrt{2y+3}+\sqrt{4-y}=4\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}2y=\dfrac{y^2+1}{x^2}\\2x=\dfrac{x^2+1}{y^2}\end{matrix}\right.\)
c,\(\left\{{}\begin{matrix}2x^2+y^2-3xy=12\\2\left(x+y\right)^2-y^2=14\end{matrix}\right.\)
Giải hệ phương trình:
1. left{{}begin{matrix}x+32sqrt{left(3y-xright)left(y+1right)}sqrt{3y-2}-sqrt{dfrac{x+5}{2}}xy-2y-2end{matrix}right.
2. left{{}begin{matrix}sqrt{2y^2-7y+10-xleft(y+3right)}+sqrt{y+1}x+1sqrt{y+1}+dfrac{3}{x+1}x+2yend{matrix}right.
3. left{{}begin{matrix}sqrt{4x-y}-sqrt{3y-4x}12sqrt{3y-4x}+yleft(5x-yright)xleft(4x+yright)-1end{matrix}right.
4. left{{}begin{matrix}9sqrt{dfrac{41}{2}left(x^2+dfrac{1}{2x+y}right)}3+40xx^2+5xy+6y4y^2+9x+9end{matrix}right.
5. left{{}begin{mat...
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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 hệ pt:
(1) \(\left\{{}\begin{matrix}x^2-3xy+2y^2=0\\3x+y=6\end{matrix}\right.\)
(2)\(\left\{{}\begin{matrix}\dfrac{x-1}{2x+1}-\dfrac{y-2}{y+2}=1\\\dfrac{3x-3}{2x+1}+\dfrac{2y-4}{y+2}=3\end{matrix}\right.\)
(3)\(\left\{{}\begin{matrix}2\left(x+y\right)+\sqrt{x+1}=4\\x+y-3\sqrt{x+1}=-5\end{matrix}\right.\)
Giải hệ phương trình sau:
a, \(\left\{{}\begin{matrix}\left(\sqrt{2}+1\right)x+y=\sqrt{2}-1\\2x-\left(\sqrt{2}-1\right)y=2\sqrt{2}\end{matrix}\right.\)
b, \(\left\{{}\begin{matrix}\sqrt{3}x-y=1\\5x+\sqrt[]{2}y=\sqrt{3}\end{matrix}\right.\)
c,\(\left\{{}\begin{matrix}2x+y=5\\3x-2y=3\end{matrix}\right.\)
Giải hệ phương trình :
1, left{{}begin{matrix}x-2y12x-y4end{matrix}right.
2, left{{}begin{matrix}frac{x}{y}-frac{y}{y+12}1frac{x}{y+12}-frac{x}{y}2end{matrix}right.
3, left{{}begin{matrix}3x^2+y^25x^2-3y1end{matrix}right.
4, left{{}begin{matrix}sqrt{3x-1}-sqrt{2y+1}12sqrt{3x-1}+3sqrt{2y+1}12end{matrix}right.
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Giải hệ phương trình :
1, \(\left\{{}\begin{matrix}x-2y=1\\2x-y=4\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}\frac{x}{y}-\frac{y}{y+12}=1\\\frac{x}{y+12}-\frac{x}{y}=2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}3x^2+y^2=5\\x^2-3y=1\end{matrix}\right.\)
4, \(\left\{{}\begin{matrix}\sqrt{3x-1}-\sqrt{2y+1}=1\\2\sqrt{3x-1}+3\sqrt{2y+1}=12\end{matrix}\right.\)
Giải hệ pt
1/left{{}begin{matrix}4xsqrt{y+1}+8xleft(4x^2-4x-3right)sqrt{x+1}dfrac{x}{x+1}+x^2left(y+2right)sqrt{left(x+1right)left(y+1right)}end{matrix}right.
2/left{{}begin{matrix}xsqrt{y^2+6}+ysqrt{x^2+3}7xyxsqrt{x^2+3}+ysqrt{y^2+6}x^2+y^2+2end{matrix}right.left{{}begin{matrix}xsqrt{y^2+6}+ysqrt{x^2+3}7xyxsqrt{x^2+3}+ysqrt{y^2+6}x^2+y^2+2end{matrix}right.
3/left{{}begin{matrix}left(2x+y-1right)left(sqrt{x+3}+sqrt{xy}+sqrt{x}right)8sqrt{x}left(sqrt{x+3}+sqrt{xy}right)^2+xy2xleft(6-xright)end...
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Giải hệ pt
1/\(\left\{{}\begin{matrix}4x\sqrt{y+1}+8x=\left(4x^2-4x-3\right)\sqrt{x+1}\\\dfrac{x}{x+1}+x^2=\left(y+2\right)\sqrt{\left(x+1\right)\left(y+1\right)}\end{matrix}\right.\)
2/\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)\(\left\{{}\begin{matrix}x\sqrt{y^2+6}+y\sqrt{x^2+3}=7xy\\x\sqrt{x^2+3}+y\sqrt{y^2+6}=x^2+y^2+2\end{matrix}\right.\)
3/\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)\(\left\{{}\begin{matrix}\left(2x+y-1\right)\left(\sqrt{x+3}+\sqrt{xy}+\sqrt{x}\right)=8\sqrt{x}\\\left(\sqrt{x+3}+\sqrt{xy}\right)^2+xy=2x\left(6-x\right)\end{matrix}\right.\)
4/\(\left\{{}\begin{matrix}\sqrt{xy+x+2}+\sqrt{x^2+x}-4\sqrt{x}=0\\xy+x^2+2=x\left(\sqrt{xy+2}+3\right)\end{matrix}\right.\)\(\left\{{}\begin{matrix}\sqrt{xy+x+2}+\sqrt{x^2+x}-4\sqrt{x}=0\\xy+x^2+2=x\left(\sqrt{xy+2}+3\right)\end{matrix}\right.\)
m.n giúp e mấy bài này vs ạ!!
Giải hệ phương trình sau: \(\left\{{}\begin{matrix}\sqrt{\dfrac{x}{y}}+\sqrt{\dfrac{y}{x}}=\dfrac{5}{2}\\x+y-5=0\end{matrix}\right.\)
Giải hệ phương trình:
1, left{{}begin{matrix}left(17-3xright)sqrt{5-x}+left(3y-14right)sqrt{4-y}02sqrt{2x+y+5}+3sqrt{3x+2y+11}x^2+6x+13end{matrix}right.
2, left{{}begin{matrix}xleft(x+yright)+sqrt{x+y}sqrt{2y}left(sqrt{2y^3}+1right)x^2y-5x^2+7left(x+yright)-46sqrt[3]{xy-x+1}end{matrix}right.
3, left{{}begin{matrix}sqrt{x}+sqrt[4]{32-x}-y^2+30sqrt[4]{x}+sqrt{32-x}+6y-240end{matrix}right.
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Giải hệ phương trình:
1, \(\left\{{}\begin{matrix}\left(17-3x\right)\sqrt{5-x}+\left(3y-14\right)\sqrt{4-y}=0\\2\sqrt{2x+y+5}+3\sqrt{3x+2y+11}=x^2+6x+13\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x\left(x+y\right)+\sqrt{x+y}=\sqrt{2y}\left(\sqrt{2y^3}+1\right)\\x^2y-5x^2+7\left(x+y\right)-4=6\sqrt[3]{xy-x+1}\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}\sqrt{x}+\sqrt[4]{32-x}-y^2+3=0\\\sqrt[4]{x}+\sqrt{32-x}+6y-24=0\end{matrix}\right.\)