Chương 3: PHƯƠNG TRÌNH, HỆ PHƯƠNG TRÌNH
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Giải hệa) left{{}begin{matrix}2x^2-5xy-y^21yleft(sqrt{xy-2y^2}+sqrt{4y^2-xy}right)1end{matrix}right.b) left{{}begin{matrix}x^3+12left(x^2-x+yright)y^3+12left(y^2-y+xright)end{matrix}right.c) left{{}begin{matrix}x^2-2y^212y^2-3z^21xy+yz+zx1end{matrix}right.left(x,y,zin Rright)}
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Giải hệ
a) \(\left\{{}\begin{matrix}2x^2-5xy-y^2=1\\y\left(\sqrt{xy-2y^2}+\sqrt{4y^2-xy}\right)=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x^3+1=2\left(x^2-x+y\right)\\y^3+1=2\left(y^2-y+x\right)\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}x^2-2y^2=1\\2y^2-3z^2=1\\xy+yz+zx=1\end{matrix}\right.\left(x,y,z\in R\right)}\)
\(\left\{{}\begin{matrix}x^2+y^2+xy=3\\y^2-xy+5x+4y=9\end{matrix}\right.\)
giải giúp mik bt này vs mn!
1)left{{}begin{matrix}2x^2+y^2+x3left(xy+1right)+2ydfrac{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+1right)sqrt{2xy+2y}yleft(3x+4y+3right)left(sqrt{x+3}-sqrt{2y-2}right)left(x-3+sqrt{x^2+x+2y-4}right)4end{matrix}right.
3)left{{}begin{matrix}x-dfrac{1}{x}y-dfrac{1}{y}2yx^3+1end{matrix}right.
4)left{{}begin{matrix}sqrt{2x-3}left(y^2+2011right)left(5-yright)+sqrt{y}yleft(y-x+2right)3x+3end{matrix}right.
5...
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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)\(\left\{{}\begin{matrix}x^3+2x^2=x^2y+2xy\\2\sqrt{x^2-2y-1}+\sqrt[3]{y^3-14=x-2}\end{matrix}\right.\)
giúp mik giải bài hệ pt vs ạ!
1,left{{}begin{matrix}x^2+y^2+dfrac{2xy}{x+y}1sqrt{x+y}x^2-yend{matrix}right.
2,left{{}begin{matrix}2x^3+xy^2+xy^3+4x^2y+2ysqrt{4x^2+x+6}-5sqrt{1+2y}1-4yend{matrix}right.
3,left{{}begin{matrix}2x^2+sqrt{2}xleft(x+yright)y+sqrt{x+y}sqrt{x-1}+xysqrt{y^2+21}end{matrix}right.
4,left{{}begin{matrix}sqrt{9y^2+left(2y+3right)left(y-xright)}+4sqrt{xy}7xleft(2y-1right)sqrt{1+x}+left(2y+1right)sqrt{1-x}2yend{matrix}right.
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giúp mik giải bài hệ pt vs ạ!
1,\(\left\{{}\begin{matrix}x^2+y^2+\dfrac{2xy}{x+y}=1\\\sqrt{x+y}=x^2-y\end{matrix}\right.\)
2,\(\left\{{}\begin{matrix}2x^3+xy^2+x=y^3+4x^2y+2y\\\sqrt{4x^2+x+6}-5\sqrt{1+2y}=1-4y\end{matrix}\right.\)
3,\(\left\{{}\begin{matrix}2x^2+\sqrt{2}x=\left(x+y\right)y+\sqrt{x+y}\\\sqrt{x-1}+xy=\sqrt{y^2+21}\end{matrix}\right.\)
4,\(\left\{{}\begin{matrix}\sqrt{9y^2+\left(2y+3\right)\left(y-x\right)}+4\sqrt{xy}=7x\\\left(2y-1\right)\sqrt{1+x}+\left(2y+1\right)\sqrt{1-x}=2y\end{matrix}\right.\)
các bạn giúp với:
1/\(\left\{{}\begin{matrix}x-2y-\sqrt{xy}=0\\\sqrt{x-1}+\sqrt{4y-1}=2\end{matrix}\right.\)
2/\(\left\{{}\begin{matrix}2x^3-9y^3=\left(x-y\right).\left(2xy+3\right)\\\left(x^2+y^2\right)=3+xy\end{matrix}\right.\)
Giải hệ phương trình
left{{}begin{matrix}x^2+y^2+xy13x^4+y^4+x^2y^291end{matrix}right.
Leftrightarrowleft{{}begin{matrix}left(x+yright)^2-xy13left(x^2+y^2right)^2-left(xyright)^291end{matrix}right.
Leftrightarrowleft{{}begin{matrix}left(x+yright)^213+xyleft[left(x+yright)^2-2xyright]^2-left(xyright)^291end{matrix}right.
Leftrightarrowleft{{}begin{matrix}left(x+yright)^2-xy13left(13-xyright)^2-left(xyright)^291end{matrix}right.
Leftrightarrowleft{{}begin{matrix}xy3left(x+yright)^216end{matri...
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Giải hệ phương trình
\(\left\{{}\begin{matrix}x^2+y^2+xy=13\\x^4+y^4+x^2y^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2-xy=13\\\left(x^2+y^2\right)^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2=13+xy\\\left[\left(x+y\right)^2-2xy\right]^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+y\right)^2-xy=13\\\left(13-xy\right)^2-\left(xy\right)^2=91\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}xy=3\\\left(x+y\right)^2=16\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=4\\xy=3\end{matrix}\right.\) hoặc x+y = -4
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x+y=4\\xy=3\end{matrix}\right.\\\left\{{}\begin{matrix}x+y=-4\\xy=3\end{matrix}\right.\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\\\left\{{}\begin{matrix}x=-3\\y=-1\end{matrix}\right.\end{matrix}\right.\)hoặc \(\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)hoặc \(\left\{{}\begin{matrix}x=-1\\y=-3\end{matrix}\right.\)
Mọi người có thể giải thích từ dấu tương đương thứ 3 xuống 4. tại sao lại như vậy k?
Giúp mình với, thanks các bạn nhiều: ^^ BT/ Giải hệ pt:
1/left{{}begin{matrix}x^3+y^31x^2y+2xy^2+y^32end{matrix}right. 2/left{{}begin{matrix}y^2left(x+8right).left(x^2+2right)y^2-4left(x+2right)y+16+16x-5x^20end{matrix}right.
3/left{{}begin{matrix}x^2-3xleft(y-1right)+y^2+yleft(x-3right)4x-xy-2y1end{matrix}right. 3/left{{}begin{matrix}sqrt{x}-sqrt{x-y-1}1y^2+x+2ysqrt{x}-xy^20end{matrix}right.
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Giúp mình với, thanks các bạn nhiều: ^^ BT/ Giải hệ pt:
1/\(\left\{{}\begin{matrix}x^3+y^3=1\\x^2y+2xy^2+y^3=2\end{matrix}\right.\) 2/\(\left\{{}\begin{matrix}y^2=\left(x+8\right).\left(x^2+2\right)\\y^2-4\left(x+2\right)y+16+16x-5x^2=0\end{matrix}\right.\)
3/\(\left\{{}\begin{matrix}x^2-3x\left(y-1\right)+y^2+y\left(x-3\right)=4\\x-xy-2y=1\end{matrix}\right.\) 3/\(\left\{{}\begin{matrix}\sqrt{x}-\sqrt{x-y-1}=1\\y^2+x+2y\sqrt{x}-xy^2=0\end{matrix}\right.\)
giải hệ phương trình:
1, \(\left\{{}\begin{matrix}\left(x+y-3\right)^3=4y^3\left(x^2y^2+xy+\frac{45}{4}\right)\\x+4y-3=2xy^2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^3+7y=\left(x+y\right)^2+x^2y+7x+4\\3x^2+y^2+8y+4=8x\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}2x+5y=xy+2\\x^2+4y+21=y^2+10x\end{matrix}\right.\)
a)left{{}begin{matrix}2left|x-6right|+3left|y-1right|55left|x-6right|-4left|y+1right|1end{matrix}right.
b) left{{}begin{matrix}2left|x+yright|-left|x-yright|93left|x+yright|+2left|x-yright|+17end{matrix}right.
c)left{{}begin{matrix}4left|x+yright|+3left|x-yright|83left|x+yright|-5left|x-yright|6end{matrix}right.
d) left{{}begin{matrix}x^2-xy242x-3y1end{matrix}right.
e) left{{}begin{matrix}3x-4y+10xy3left(x+yright)-9end{matrix}right.
f) left{{}begin{matrix}2x+3y53x^2-y^2+2y4end{matrix}right.
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a)\(\left\{{}\begin{matrix}2\left|x-6\right|+3\left|y-1\right|=5\\5\left|x-6\right|-4\left|y+1\right|=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}2\left|x+y\right|-\left|x-y\right|=9\\3\left|x+y\right|+2\left|x-y\right|+17\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}4\left|x+y\right|+3\left|x-y\right|=8\\3\left|x+y\right|-5\left|x-y\right|=6\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}x^2-xy=24\\2x-3y=1\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}3x-4y+1=0\\xy=3\left(x+y\right)-9\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}2x+3y=5\\3x^2-y^2+2y=4\end{matrix}\right.\)