Question

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 !

Answer 1

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

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