\(\left\{{}\begin{matrix}\left|x\right|\left(4y+1\right)-2y=-3\\\left|x\left(x^2-12y\right)\right|+4y^2=9\end{matrix}\right.\)
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Giải hệ :
\(\left\{{}\begin{matrix}x^2\left(4y+1\right)-2y=-3\\x^2\left(x^2-12y\right)+4y^2=9\end{matrix}\right.\)
hpt \(\Leftrightarrow\left\{{}\begin{matrix}x^2\left(4y+1\right)=2y-3\\x^2\left(x^2-12y\right)=-4y^2+9\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^2\left(4y+1\right)\left(2y+3\right)=4y^2-9\\x^2\left(x^2-12y\right)=-4y^2+9\end{matrix}\right.\)
Cộng theo vế 2 pt ta đc:
\(x^2\left(x^2+8y^2+2y+3\right)=0\)
\(\Leftrightarrow x^2\left[x^2+7y^2+\left(y+1\right)^2+2\right]=0\)
\(\Leftrightarrow x=0\)
\(\Rightarrow y=\dfrac{3}{2}\left(tm\right)\)
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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 phương trình:
1, \(\left\{{}\begin{matrix}2+6y=\frac{x}{y}-\sqrt{x-2y}\\\sqrt{x+\sqrt{x-2y}}=x+3y-2\end{matrix}\right.\)
2, \(\left\{{}\begin{matrix}x^2+y^2+xy+1=4y\\y\left(x+y\right)^2=2x^2-7y+2\end{matrix}\right.\)
3, \(\left\{{}\begin{matrix}x^2\left(y+1\right)=6y-2\\x^4y^2+2x^2y^2+y\left(x^2+1\right)=12y^2-1\end{matrix}\right.\)
\(\left\{{}\begin{matrix}4y^3-12y^2+13y-5=\left(4x+9\right)\sqrt{x+2}\\2\left(x^2-5\left(y-1^2\right)\right)=3\left(y-1\right)\sqrt{x^2-4x-8}\end{matrix}\right.\)
1/ Giải hpt = p đặt ẩn phụ : a,\(\left\{{}\begin{matrix}\left(x+y\right)^3+y=5\\3\left(x+y\right)^3-22xy+21=11x^2+12y^3\end{matrix}\right.\)
b,\(\left\{{}\begin{matrix}81x^3y^2-81x^2y^2+33xy^2-29y^2=4\\25y^3+9x^2y^3-6xy^3-4y^2=24\end{matrix}\right.\)
30 tháng 4 2021 lúc 16:32
B4:Giải hệ pt:a)left{{}begin{matrix}4x+2y142x-2y4end{matrix}right.b)left{{}begin{matrix}2x-4y03x+2y8end{matrix}right.c)left{{}begin{matrix}2left(x+yright)+3left(x-yright)4left(x+yright)+2left(x-yright)5end{matrix}right.d)left{{}begin{matrix}dfrac{1}{x}+dfrac{1}{y}dfrac{1}{12}dfrac{8}{x}+dfrac{15}{y}1end{matrix}right.
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B4:Giải hệ pt:
a)\(\left\{{}\begin{matrix}4x+2y=14\\2x-2y=4\end{matrix}\right.\)
b)\(\left\{{}\begin{matrix}2x-4y=0\\3x+2y=8\end{matrix}\right.\)
c)\(\left\{{}\begin{matrix}2\left(x+y\right)+3\left(x-y\right)=4\\\left(x+y\right)+2\left(x-y\right)=5\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{12}\\\dfrac{8}{x}+\dfrac{15}{y}=1\end{matrix}\right.\)
a.\(\left\{{}\begin{matrix}4x+2y=14\\2x-2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}6x=18\\2x-2y=4\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=2\\4-2y=4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\-2y=0\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=2\\y=0\end{matrix}\right.\)
vậy hệ pt có ndn \(\left\{2;0\right\}\)
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b.\(\left\{{}\begin{matrix}2x-4y=0\\3x+2y=8\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}2x-4y=0\\6x+4y=16\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}8x=16\\2x-4y=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\4-4y=0\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}x=2\\-4y=-4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
vậy hệ pt có ndn \(\left\{2;1\right\}\)
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d.\(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{12}\\\dfrac{8}{x}+\dfrac{15}{y}=1\end{matrix}\right.\)
đặt \(\dfrac{1}{x}=a;\dfrac{1}{y}=b\) ta có hệ pt:
\(\left\{{}\begin{matrix}a+b=\dfrac{1}{12}\\8a+15b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}8a+8b=\dfrac{2}{3}\\8a+15b=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}7b=\dfrac{1}{3}\\8a+15b=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=\dfrac{1}{21}\\8a+15\times\dfrac{1}{21}=1\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}b=\dfrac{1}{21}\\8a+\dfrac{5}{7}=1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}b=\dfrac{1}{21}\\8a=\dfrac{2}{7}\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}b=\dfrac{1}{21}\\a=\dfrac{1}{28}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}\dfrac{1}{y}=\dfrac{1}{21}\\\dfrac{1}{x}=\dfrac{1}{28}\end{matrix}\right.\)
⇔\(\left\{{}\begin{matrix}y=21\\x=28\end{matrix}\right.\)
vậy hệ pt có ndn\(\left\{28;21\right\}\)
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\(\left\{{}\begin{matrix}x^2\left(y+1\right)=6y-2\\x^4y^2+2x^2y^2+2\left(x^2+1\right)=12y^2-1\end{matrix}\right.\)
Giải hệ phương trình
left{{}begin{matrix}4left(2x-y+3right)-3left(x-2y+3right)483left(3x-4y+3right)+4left(4x-2y-9right)48end{matrix}right.
left{{}begin{matrix}6left(x+yright)8+2x-3y5left(y-xright)5+3x+2yend{matrix}right.
left{{}begin{matrix}-2left(2x+1right)+1,53left(y-2right)-6x11,5-4left(3-xright)2y-left(5-xright)end{matrix}right.
left{{}begin{matrix}dfrac{8x-5y-3}{7}+dfrac{11y-4x-7}{5}12dfrac{9x+4y-13}{5}-dfrac{3left(x-2right)}{4}15end{matrix}right.
left{{}begin{matrix}2sqrt{3}x-sqrt{5}y2...
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Giải hệ phương trình
\(\left\{{}\begin{matrix}4\left(2x-y+3\right)-3\left(x-2y+3\right)=48\\3\left(3x-4y+3\right)+4\left(4x-2y-9\right)=48\end{matrix}\right.\)
\(\left\{{}\begin{matrix}6\left(x+y\right)=8+2x-3y\\5\left(y-x\right)=5+3x+2y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}-2\left(2x+1\right)+1,5=3\left(y-2\right)-6x\\11,5-4\left(3-x\right)=2y-\left(5-x\right)\end{matrix}\right.\)
\(\left\{{}\begin{matrix}\dfrac{8x-5y-3}{7}+\dfrac{11y-4x-7}{5}=12\\\dfrac{9x+4y-13}{5}-\dfrac{3\left(x-2\right)}{4}=15\end{matrix}\right.\)
\(\left\{{}\begin{matrix}2\sqrt{3}x-\sqrt{5}y=2\sqrt{6}-\sqrt{15}\\3x-y=3\sqrt{2}-\sqrt{3}\end{matrix}\right.\)
a: \(\Leftrightarrow\left\{{}\begin{matrix}8x-4y+12-3x+6y-9=48\\9x-12y+9+16x-8y-36=48\end{matrix}\right.\)
=>5x+2y=48-12+9=45 và 25x-20y=48+36-9=48+27=75
=>x=7; y=5
b: \(\Leftrightarrow\left\{{}\begin{matrix}6x+6y-2x+3y=8\\-5x+5y-3x-2y=5\end{matrix}\right.\)
=>4x+9y=8 và -8x+3y=5
=>x=-1/4; y=1
c: \(\Leftrightarrow\left\{{}\begin{matrix}-4x-2+1,5=3y-6-6x\\11,5-12+4x=2y-5+x\end{matrix}\right.\)
=>-4x-0,5=-6x+3y-6 và 4x-0,5=x+2y-5
=>2x-3y=-5,5 và 3x-2y=-4,5
=>x=-1/2; y=3/2
e: \(\Leftrightarrow\left\{{}\begin{matrix}x\cdot2\sqrt{3}-y\sqrt{5}=2\sqrt{3}\cdot\sqrt{2}-\sqrt{5}\cdot\sqrt{3}\\3x-y=3\sqrt{2}-\sqrt{3}\end{matrix}\right.\)
=>\(x=\sqrt{2};y=\sqrt{3}\)
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\(\left\{{}\begin{matrix}x^3-y^3=9\\x^2+2y^2=x-4y\end{matrix}\right.\left\{{}\begin{matrix}\left(x-y\right)\left(2x+3y\right)=12\\6\left(x-y\right)+xy\left(x-y\right)=12\end{matrix}\right.GiaihePT\)
a/ Lấy pt trên trừ 3 lần pt dưới
b/ \(2x+3y=6+xy\Leftrightarrow\left(2x-6\right)-\left(xy-3y\right)=0\)
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