Question

Реши систему уравнений:

Answer 1

$\frac{1}{x+y}=u, \frac{1}{x+y}=v;\\\\\left \{ {{u+v=11} \atop {4u+2v=30}} \right. \\\\\left \{ {{v=11-u} \atop {4u-2u+22=30}} \right. \left \{ {{2u=8} \atop {v=11-u}} \right. \left \{ {{u=4} \atop {v=7}} \right. \\\\\left \{ {{\frac{1}{x+y}=4 } \atop {\frac{1}{x-y}=7 }} \right. \left \{ {{x+y=\frac{1}{4} } \atop {x-y=\frac{1}{7} }} \right. +\\\\2x=\frac{1}{4}+\frac{1}{7}\\\\2x=\frac{11}{28} \\\\x=\frac{11}{56} \\\frac{11}{56}+y=\frac{1}{4}\Rightarrow y=\frac{1}{4}-\frac{11}{56}=\frac{3}{56}$

ОТВЕТ: $(\frac{11}{56} ;\frac{3}{56} )$