x+4xy+y=6x^2y+xy^2=2это системаОЧЕНЬ СРОЧНО . Created by sirniks2012. algebra-ru

x+4xy+y=6x^2y+xy^2=2это системаОЧЕНЬ СРОЧНО ...

sirniks2012 @sirniks2012

July 2022 1 12 Report

x+4xy+y=6
x^2y+xy^2=2
это система
ОЧЕНЬ СРОЧНО

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$x+4xy+y=6\\
x^2y+xy^2=2\\
\\
x+y+4xy=6\\
xy(x+y)=2\\
\\
x+y=6-4xy\\
xy(6-4xy)=2\\
\\
xy=t\\
6t-4t^2=2\\
4t^2-6t+2=0\\
D=36-4*4*2=2^2\
t_{1}=\frac{6+2}{8}=1\\
t_{2}=\frac{6-2}{8}=\frac{1}{2}\\
xy=1\\
xy=0.5$

$xy=1\\
xy=0.5\\
\\
1)\\
x+4xy+y=6\\
xy=1\\
\\
x=\frac{1}{y}\\
\frac{1}{y}+4+y=6\\
4y+y^2-6y+1=0\\
y^2-2y+1=0\\
(y-1)^2=0\\
y=1\\
x=1\\
\\
2)\\
x+4xy+y=6\\
xy=0.5\\
\\
x=\frac{0.5}{y}\\
\frac{0.5}{y}+4*0.5+y=6\\
0.5+2y+y^2-6y=0\\
y^2-4y+0.5=0\\
D=\sqrt{56}\\
y_{1}=-\frac{\sqrt{14}-4}{2}\\
y_{2}=\frac{\sqrt{14}+4}{2}\\
x_{1}=-\frac{\sqrt{14}+8}{4\sqrt{14}-18}\\
x_{2}=-\frac{ \sqrt{14}-8}{4\sqrt{14}+18}$

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