4Помогите пожалуйста!...

July 2022 1 12 Report

Решите системы уравнений:
1) 2\ x-y + 6/x+y=1.1
4\x-y-9\x+y=0.1

2) 1/x+1/y=3/2
1\x^2=1\y^2=5/4

Помогите пожалуйста!

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$\left \{ {{\frac{2}{x-y}+\frac{6}{x+y}=1.1} \atop {\frac{4}{x-y}-\frac{9}{x+y}=0.1}} \right.\\
\\
zamena\\ 
x-y=a\\
x+y=b\\
\\
 \left \{ {{\frac{2}{a}+\frac{6}{b}=1.1} \atop {\frac{4}{a}-\frac{9}{b}=0.1}} \right.\\
 \\
\left \{ {{2b+6a=1.1ab\\} \atop {4b-9a=0.1ab}} \right.\\
\\
 \left \{ {{y=2} \atop {x=2}} \right. \\
a=4\\
b=10\\

 
$
$\left \{ {{x-y=4\\
} \atop {x+y=10}} \right. \\
\\
4+2y=10\\
2y=6\\
y=3\\
x=7\\
$

$2)
 \left \{ {{\frac{1}{x}+\frac{1}{y}=\frac{3}{2}} \atop {\frac{1}{x^2}+\frac{1}{y^2}=\frac{5}{4}}} \right. \\
\\
\frac{1}{x}=a\\
\frac{1}{y}=b\\
 \left \{ {{a+b=1.5} \atop {a^2+b^2=1.25}} \right. \\
\\
(a+b)^2=a^2+2ab+b^2=2.25\\
2ab=1\\
a+b=1.5\\
ab=0.5\\
\\
a=1\\ b=0.5\\
x=1\\
y=2\\
$

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