Question

решить систему 1/x+1/y=3/4 и (x^2+y^2)/(x+y)=10/3

Answer 1

$left { {{ frac{1}{x}+frac{1}{y}=frac{3}{4} } atop { frac{x^2+y^2}{x+y} = frac{10}{3} }} right. \ left { {{ frac{x+y}{xy}=frac{3}{4} } atop { frac{x^2+y^2+2xy-2xy}{x+y} = frac{10}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { frac{(x+y)^2-2xy}{x+y} = frac{10}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { frac{(x+y)^2}{x+y}-frac{2xy}{x+y} = frac{10}{3} }} right.$
$left { {{ frac{xy}{x+y}=frac{4}{3} } atop { (x+y)-2frac{xy}{x+y} = frac{10}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { (x+y)-2*frac{4}{3} = frac{10}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { (x+y)-frac{8}{3} = frac{10}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { x+y=frac{10}{3}+frac{8}{3} }} right. \ left { {{ frac{xy}{x+y}=frac{4}{3} } atop { x+y=frac{18}{3} }} right.$
$left { {{ frac{xy}{x+y}=frac{4}{3} } atop { x+y=6 }} right. \ left { {{ frac{xy}{6}=frac{4}{3} } atop { x+y=6 }} right. \ left { {{ xy=frac{4}{3}*6 } atop { x+y=6 }} right. \ left { {{ xy=8 } atop { x+y=6 }} right. \ left { {{ x(6-x)=8 } atop { y=6-x }} right. \ left { {{ x6-x^2=8 } atop { y=6-x }} right. \ left { {{ x_{1}=2; x_{2}=4 } atop { y=6-x }} right. \ left { {{ x_{1}=2; x_{2}=4 } atop { y_{1}=4; y_{2}=2 }} right.$