Question

Как решить систему во вложении?

Answer 1

привести к общему знаменателю (x <> y ___ x <> -y ___ y <> 0 ___ <>===не равно)

12(x^2-y^2) = 48(xy-y^2) + 36(xy+y^2) ___ 48(x-y) + 48(x+y) = 7(x^2-y^2)

x^2-y^2 = 4xy - 4y^2 + 3xy + 3y^2 ___ 48x - 48y + 48x + 48y = 7(x^2-y^2)

x^2 = 7xy ___ 96x = 7(x^2-y^2)

x^2 - 7xy = 0 ___ 96x = 7(x^2-y^2)

x(x - 7y) = 0 ___ 96x = 7(x^2-y^2)

x = 0 ___ 0 = -7y^2 => y = 0---не удовлетворяет ОДЗ

x = 7y ___ 96*7y = 7(49y^2-y^2) => 96*y = 48y^2 => 2y = y^2 => y=2 (y не равно 0) => x=14

 

Answer 2

$left { {{frac{12}{y}=frac{48}{x+y}+frac{36}{x-y}} atop {frac{48}{x+y} +frac{48}{x-y}=7}} right.$

$left { {{frac{12}{y}=frac{48(x-y)+36(x+y)}{x^2-y^2}} atop {frac{48(x-y)+48(x+y)}{x^2-y^2}=7}} right.$

$left { {{frac{12}{y}=frac{48x-48y+36x+36y}{x^2-y^2}} atop {frac{48x-48y+48x+48y}{x^2-y^2}=7}} right.$

$left { {{frac{12}{y}=frac{84x-12y}{x^2-y^2}} atop {frac{96x}{x^2-y^2}=7}} right.$

$left { {{frac{1}{y}=frac{7x-y}{x^2-y^2}} atop {96x=7x^2-7y^2} right.$

$left { {x^2-y^2=7xy-y^2} atop {96x=7x^2-7y^2} right.$

$left { {x^2=7xy} atop {96x=7x^2-7y^2} right.$

$left { y=frac{1}{7}x} atop {96x=7x^2-7y^2} right.$

$left { y=frac{1}{7}x} atop {96x=7x^2-7(frac{1}{7}x)^2} right.$

Решим второе уравнение

$96x=7x^2-frac{1}{7}x^2$

$96x=frac{48}{7}x^2$

$frac{48}{7}x=96$

х=14

$y=frac{1}{7}*14=2$

................................................................................................