Question

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

2) 1/x+1/y=3/2
    1x^2=1y^2=5/4

Помогите пожалуйста!

Answer 1

$left { {{frac{2}{x-y}+frac{6}{x+y}=1.1} atop {frac{4}{x-y}-frac{9}{x+y}=0.1}} right.\ \ zamena\ x-y=a\ x+y=b\ \ left { {{frac{2}{a}+frac{6}{b}=1.1} atop {frac{4}{a}-frac{9}{b}=0.1}} right.\ \ left { {{2b+6a=1.1ab\} atop {4b-9a=0.1ab}} right.\ \ left { {{y=2} atop {x=2}} right. \ a=4\ b=10$
$left { {{x-y=4\ } atop {x+y=10}} right. \ \ 4+2y=10\ 2y=6\ y=3\ x=7$

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