Giải hệ phương trình
\(\left\{{}\begin{matrix}\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{7}{\sqrt{xy}}+1\\\sqrt{x^3y}+\sqrt{y^3x}=78\end{matrix}\right.\)
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giải hệ phương trình: \(\left\{{}\begin{matrix}\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=\frac{7}{\sqrt{xy}}+1\\\sqrt{x^3y}+\sqrt{xy^3}=78\end{matrix}\right.\)
1.Giải hệ phương trình:
a.left{{}begin{matrix}2sqrt{2}x+y2sqrt{2}7x-3y7end{matrix}right.
b.left{{}begin{matrix}7x+y-frac{1}{7}-frac{4}{3}x-2y1frac{1}{3}end{matrix}right.
c.left{{}begin{matrix}2sqrt{5}x+3ysqrt{2}sqrt{5}x-y3sqrt{2}end{matrix}right.
d.left{{}begin{matrix}frac{2}{x}+frac{3}{y}-5frac{3}{x}-frac{4}{y}1end{matrix}right.
e.left{{}begin{matrix}-frac{5}{3x+1}+frac{7}{2x+1}frac{5}{7}frac{1}{3x+1}-frac{1}{2y-3}frac{2}{7}end{matrix}right.
g.left{{}begin{matrix}2x^2+5y^2129-3x^2+y^213en...
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1.Giải hệ phương trình:
a.\(\left\{{}\begin{matrix}2\sqrt{2}x+y=2\sqrt{2}\\7x-3y=7\end{matrix}\right.\)
b.\(\left\{{}\begin{matrix}7x+y=-\frac{1}{7}\\-\frac{4}{3}x-2y=1\frac{1}{3}\end{matrix}\right.\)
c.\(\left\{{}\begin{matrix}2\sqrt{5}x+3y=\sqrt{2}\\\sqrt{5}x-y=3\sqrt{2}\end{matrix}\right.\)
d.\(\left\{{}\begin{matrix}\frac{2}{x}+\frac{3}{y}=-5\\\frac{3}{x}-\frac{4}{y}=1\end{matrix}\right.\)
e.\(\left\{{}\begin{matrix}-\frac{5}{3x+1}+\frac{7}{2x+1}=\frac{5}{7}\\\frac{1}{3x+1}-\frac{1}{2y-3}=\frac{2}{7}\\\end{matrix}\right.\)
g.\(\left\{{}\begin{matrix}2x^2+5y^2=129\\-3x^2+y^2=13\end{matrix}\right.\)
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, \(\left\{{}\begin{matrix}\sqrt{3x-1}-\sqrt{2y+1}=1\\2\sqrt{3x-1}+3\sqrt{2y+1}=12\end{matrix}\right.\)
a/ Bạn tự giải
b/ ĐKXĐ:...
Cộng vế với vế: \(\frac{x-y}{y+12}=3\Rightarrow x-y=3y+36\Rightarrow x=4y+36\)
Thay vào pt đầu: \(\frac{4y+36}{y}-\frac{y}{y+12}=1\)
Đặt \(\frac{y+12}{y}=a\Rightarrow4a-\frac{1}{a}=1\Rightarrow4a^2-a-1=0\)
\(\Rightarrow a=\frac{1\pm\sqrt{17}}{8}\) \(\Rightarrow\frac{y+12}{y}=\frac{1\pm\sqrt{17}}{8}\)
\(\Rightarrow\left[{}\begin{matrix}y+12=y\left(\frac{1+\sqrt{17}}{8}\right)\\y+12=y\left(\frac{1-\sqrt{17}}{8}\right)\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\left(\frac{-7+\sqrt{17}}{8}\right)y=12\\\left(\frac{-7-\sqrt{17}}{8}\right)y=12\end{matrix}\right.\) \(\Rightarrow y=...\)
Chắc bạn ghi sai đề, nghiệm quá xấu
3/ \(\Leftrightarrow\left\{{}\begin{matrix}3x^2+y^2=5\\3x^2-9y=3\end{matrix}\right.\) \(\Rightarrow y^2+9y=2\Rightarrow y^2+9y-2=0\Rightarrow y=...\)
4/ ĐKXĐ:...
\(\Leftrightarrow\left\{{}\begin{matrix}3\sqrt{3x-1}-3\sqrt{2y+1}=3\\2\sqrt{3x-1}+3\sqrt{2y+1}=12\end{matrix}\right.\)
\(\Rightarrow5\sqrt{3x-1}=15\Rightarrow\sqrt{3x-1}=3\Rightarrow x=\frac{10}{3}\)
\(\sqrt{2y+1}=\sqrt{3x-1}-1=3-1=2\Rightarrow2y+1=4\Rightarrow y=\frac{3}{2}\)
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3 tháng 12 2019 lúc 20:10
Giải hệ:
left{{}begin{matrix}x^2+y^2+xy527x^3+6y^2x2+y^3+30x^2yend{matrix}right.
left{{}begin{matrix}x^2+y^2+frac{8xy}{x+y}16frac{x^2}{8y}+frac{2x}{3}sqrt{frac{x^3}{3y}+frac{x^2}{4}}-frac{y}{2}end{matrix}right., left{{}begin{matrix}frac{1}{3x}+frac{2x}{3y}frac{x+sqrt{y}}{2x^2+y}2left(2x+sqrt{y}right)sqrt{2x+6}-yend{matrix}right.
left{{}begin{matrix}x^2y-3x-13xsqrt{y}left(sqrt{1-x}-1right)^3sqrt{8x^2-3xy+4y^2}+sqrt{xy}4yend{matrix}right.
Cho các số a,b,c là các số k âm sao cho tổng hai số bất...
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Giải hệ:
\(\left\{{}\begin{matrix}x^2+y^2+xy=5\\27x^3+6y^2x=2+y^3+30x^2y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x^2+y^2+\frac{8xy}{x+y}=16\\\frac{x^2}{8y}+\frac{2x}{3}=\sqrt{\frac{x^3}{3y}+\frac{x^2}{4}}-\frac{y}{2}\end{matrix}\right.\), \(\left\{{}\begin{matrix}\frac{1}{3x}+\frac{2x}{3y}=\frac{x+\sqrt{y}}{2x^2+y}\\2\left(2x+\sqrt{y}\right)=\sqrt{2x+6}-y\end{matrix}\right.\)
\(\left\{{}\begin{matrix}x^2y-3x-1=3x\sqrt{y}\left(\sqrt{1-x}-1\right)^3\\\sqrt{8x^2-3xy+4y^2}+\sqrt{xy}=4y\end{matrix}\right.\)
Cho các số a,b,c là các số k âm sao cho tổng hai số bất kì đều dương.CMR \(\sqrt{\frac{a}{b+c}}+\sqrt{\frac{b}{c+a}}+\sqrt{\frac{c}{a+b}}+\frac{16\sqrt{ab+bc+ac}}{a+b+c}\ge8\)
Ai phát hiện sai đề thì sửa và làm giúp mk hộ với, cảm ơn :) (chỉ cần làm tóm tắt thôi)
Giải hệ pt:
a)left{{}begin{matrix}x^2+y^2+x+y18xleft(x+1right).yleft(y+1right)72end{matrix}right. b) left{{}begin{matrix}frac{1}{x}+frac{1}{y+1}13y-1xyend{matrix}right. c)left{{}begin{matrix}2x+3yxy+5frac{1}{x}+frac{1}{y+1}1end{matrix}right.
d)left{{}begin{matrix}sqrt{frac{x}{y}}-3sqrt{frac{y}{x}}2x-y+xy1end{matrix}right. e)left{{}begin{matrix}xy+x+yx^2-2y^2xsqrt{2y}-ysqrt{x-1}2x-2yend{matrix}right.
HELP ME :((
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Giải hệ pt:
a)\(\left\{{}\begin{matrix}x^2+y^2+x+y=18\\x\left(x+1\right).y\left(y+1\right)=72\end{matrix}\right.\) b) \(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y+1}=1\\3y-1=xy\end{matrix}\right.\) c)\(\left\{{}\begin{matrix}2x+3y=xy+5\\\frac{1}{x}+\frac{1}{y+1}=1\end{matrix}\right.\)
d)\(\left\{{}\begin{matrix}\sqrt{\frac{x}{y}}-3\sqrt{\frac{y}{x}}=2\\x-y+xy=1\end{matrix}\right.\) e)\(\left\{{}\begin{matrix}xy+x+y=x^2-2y^2\\x\sqrt{2y}-y\sqrt{x-1}=2x-2y\end{matrix}\right.\)
HELP ME :((
a/ \(\left\{{}\begin{matrix}\left(x^2+x\right)+\left(y^2+y\right)=18\\\left(x^2+x\right)\left(y^2+y\right)=72\end{matrix}\right.\)
Theo Viet đảo, \(x^2+x\) và \(y^2+y\) là nghiệm của:
\(t^2-18t+72=0\Rightarrow\left[{}\begin{matrix}t=12\\t=6\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x^2+x=6\\y^2+y=12\end{matrix}\right.\\\left\{{}\begin{matrix}x^2+x=12\\y^2+y=6\end{matrix}\right.\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}\left\{{}\begin{matrix}x=\left\{2;-3\right\}\\y=\left\{3;-4\right\}\end{matrix}\right.\\\left\{{}\begin{matrix}x=\left\{3;-4\right\}\\y=\left\{2;-3\right\}\end{matrix}\right.\end{matrix}\right.\)
b/ ĐKXĐ: ...
\(\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y+1}=1\\x=\frac{3y-1}{y}\end{matrix}\right.\)
Nhận thấy \(y=\frac{1}{3}\) không phải nghiệm
\(\Rightarrow\left\{{}\begin{matrix}\frac{1}{x}+\frac{1}{y+1}=1\\\frac{1}{x}=\frac{y}{3y-1}\end{matrix}\right.\) \(\Rightarrow\frac{y}{3y-1}+\frac{1}{y+1}=1\)
\(\Leftrightarrow y\left(y+1\right)+3y-1=\left(3y-1\right)\left(y+1\right)\)
\(\Leftrightarrow y^2-y=0\Rightarrow\left[{}\begin{matrix}y=0\left(l\right)\\y=1\end{matrix}\right.\) \(\Rightarrow x=2\)
c/ ĐKXĐ: ...
\(\Leftrightarrow\left\{{}\begin{matrix}2x+3y=xy+5\\y+1=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+2y-1=5\\y+1=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=3\\y+1=xy\end{matrix}\right.\)
\(\Rightarrow y+1=\left(3-y\right)y\)
\(\Leftrightarrow y^2-2y+1=0\Rightarrow y=1\Rightarrow x=2\)
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giải hệ: a, left{{}begin{matrix}x^2+frac{1}{y^2}+frac{x}{y}3x+frac{1}{y}+frac{x}{y}3end{matrix}right.
b, left{{}begin{matrix}sqrt[]{x-1}+sqrt[]{y-1}2frac{1}{x}+frac{1}{y}1end{matrix}right.
c,left{{}begin{matrix}xsqrt[]{x}+ysqrt[]{y}35xsqrt[]{y}+ysqrt[]{x}30end{matrix}right.
d,left{{}begin{matrix}x^2+xy+y^23x+xy+y-1end{matrix}right.
e,left{{}begin{matrix}left(frac{x}{y}right)^3+left(frac{x}{y}right)^212left(xyright)^2+xy6end{matrix}right.
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giải hệ: a, \(\left\{{}\begin{matrix}x^2+\frac{1}{y^2}+\frac{x}{y}=3\\x+\frac{1}{y}+\frac{x}{y}=3\end{matrix}\right.\)
b, \(\left\{{}\begin{matrix}\sqrt[]{x-1}+\sqrt[]{y-1}=2\\\frac{1}{x}+\frac{1}{y}=1\end{matrix}\right.\)
c,\(\left\{{}\begin{matrix}x\sqrt[]{x}+y\sqrt[]{y}=35\\x\sqrt[]{y}+y\sqrt[]{x}=30\end{matrix}\right.\)
d,\(\left\{{}\begin{matrix}x^2+xy+y^2=3\\x+xy+y=-1\end{matrix}\right.\)
e,\(\left\{{}\begin{matrix}\left(\frac{x}{y}\right)^3+\left(\frac{x}{y}\right)^2=12\\\left(xy\right)^2+xy=6\end{matrix}\right.\)
\(e,\left\{{}\begin{matrix}\left(\frac{x}{y}\right)^3+\left(\frac{x}{y}\right)^2=12\\\left(xy\right)^2+xy=6\end{matrix}\right.\left(x;y\ne0\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}\frac{x}{y}=2\\xy\in\left\{2;-3\right\}\end{matrix}\right.\)
Vì \(\frac{x}{y}=2>0\Rightarrow xy>0\Rightarrow xy=2\)
\(\Rightarrow\left\{{}\begin{matrix}\frac{x}{y}=2\\xy=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2y\\2y^2=2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\left(h\right)\left\{{}\begin{matrix}x=-2\\y=-1\end{matrix}\right.\)
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\(a,\left\{{}\begin{matrix}x^2+\frac{1}{y^2}+\frac{x}{y}=3\\x+\frac{1}{y}+\frac{x}{y}=3\end{matrix}\right.\left(x;y\ne0\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(x+\frac{1}{y}\right)^2-\frac{x}{y}=3\\\left(x+\frac{1}{y}\right)+\frac{x}{y}=3\end{matrix}\right.\)
Đặt \(\left\{{}\begin{matrix}x+\frac{1}{y}=a\\\frac{x}{y}=b\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}a^2-b=3\\a+b=3\end{matrix}\right.\)
Làm nốt nha
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\(\left\{{}\begin{matrix}\sqrt{x-1}+\sqrt{y-1}=2\\\frac{1}{x}+\frac{1}{y}=1\end{matrix}\right.\left(x;y\ge1\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y-2+2\sqrt{\left(x-1\right)\left(y-1\right)}=4\\x+y=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+2\sqrt{xy-\left(x+y\right)+1}=6\\x+y=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y+2\sqrt{xy-xy+1}=6\\x+y=xy\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x+y=4\\xy=4\end{matrix}\right.\)
Làm nốt
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Xem thêm câu trả lời
giải hệ:
a) left{{}begin{matrix}sqrt{x+3y}+sqrt{x+y}2sqrt{x+y}+y-x1end{matrix}right.
b) left{{}begin{matrix}x+y+frac{1}{x}+frac{1}{y}4x^2+y^2+frac{1}{x^2}+frac{1}{y^2}4end{matrix}right.
c) left{{}begin{matrix}left(x-frac{1}{y}right)left(y+frac{1}{x}right)22x^2y+xy^2-4xy2x-yend{matrix}right.
d) left{{}begin{matrix}2x^2+xyy^2-3y+2x^2-y^23end{matrix}right.
e) left{{}begin{matrix}x^2+y^2+z^2+2xy-xz-zy3x^2+y^2-2xy-xz+zy-1end{matrix}right.
f) left{{}begin{matrix}x^2-y^2+5x-y+60x^2+left(x-yright)...
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giải hệ:
a) \(\left\{{}\begin{matrix}\sqrt{x+3y}+\sqrt{x+y}=2\\\sqrt{x+y}+y-x=1\end{matrix}\right.\)
b) \(\left\{{}\begin{matrix}x+y+\frac{1}{x}+\frac{1}{y}=4\\x^2+y^2+\frac{1}{x^2}+\frac{1}{y^2}=4\end{matrix}\right.\)
c) \(\left\{{}\begin{matrix}\left(x-\frac{1}{y}\right)\left(y+\frac{1}{x}\right)=2\\2x^2y+xy^2-4xy=2x-y\end{matrix}\right.\)
d) \(\left\{{}\begin{matrix}2x^2+xy=y^2-3y+2\\x^2-y^2=3\end{matrix}\right.\)
e) \(\left\{{}\begin{matrix}x^2+y^2+z^2+2xy-xz-zy=3\\x^2+y^2-2xy-xz+zy=-1\end{matrix}\right.\)
f) \(\left\{{}\begin{matrix}x^2-y^2+5x-y+6=0\\x^2+\left(x-y\right)^2=2+\sqrt{6x+7}+2\sqrt{x+y+1}\end{matrix}\right.\)
giải hệ pt:
\(\left\{{}\begin{matrix}\frac{1}{\sqrt{x}}-\frac{\sqrt{x}}{y}=x^2+xy-2y^2\\\left(\sqrt{x+3}-\sqrt{y}\right)\left(1+\sqrt{x^2+3x}\right)=3\end{matrix}\right.\)
ĐKXĐ x ; y > 0
(1) \(\Rightarrow\left(y-x\right)\left(\frac{1}{\sqrt{x}y}+x+2xy\right)=0\)
\(\Rightarrow x=y\)
\(\Rightarrow...\)
#Kaito#
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giải hệ phương trình
\(\left\{{}\begin{matrix}x\sqrt{x}-3y\sqrt{x}=10\\y\sqrt{y}-3x\sqrt{y}=5\end{matrix}\right.\)