Question

Помогите,алгебра!!!Любое из заданий

Answer 1

$left { {{2 sqrt{x} -2 sqrt{y} = sqrt{xy} } atop {x+y=5}} right. \ \ x geq 0;y geq 0;x geq y \ \ left { {{4x+4y-8 sqrt{xy} =xy} atop {x+y=5}} right. \ \ left { {{4(x+y)-8 sqrt{xy} =xy} atop {x+y=5}} right. \ \ left { {{xy+8 sqrt{xy} -20=0} atop {x+y=5}} right. \ \ t= sqrt{xy} ;t geq 0 \ \ t^2+8t-20=0 \ \ t^2-2t+10t-20=0 \ \ t(t-2)+10(t-2)=0 \ \ (t-2)(t+10)=0 \ \ t geq 0;t=2; sqrt{xy}=2;xy=4$
$left { {x{y=4} atop {x+y=5}} right. \ \ x(5-x)=4 \ \ x^2-5x+4=0 \ \ x^2-x-4x+4=0 \ \ x(x-1)-4(x-1)=0 \ \ (x-1)(x-4)=0 \ \ 1)x=4;y=1;x textgreater y \ \ 2)x=1;y=4;x textless y$
не удовлетворяет условию x≥y

ОТВЕТ (4;1)