Question

Помогите решить пожалуйста!!!!!!!!!!!!!!

Answer 1

$left { {{ sqrt{frac{y}{x}} - 2 sqrt{frac{x}{y}} = 1 ,} atop { sqrt{5x+y} + sqrt{5x-y} = 4;}} right. left { {{ (sqrt{frac{y}{x}} - 2 sqrt{frac{x}{y}})^2 = 1 , } atop { (sqrt{5x+y} + sqrt{5x-y})^2 = 4^2 ; }} right.$
$left { {{ frac{y}{x} - 4 sqrt{frac{y}{x}}sqrt{frac{x}{y}} +4frac{x}{y} = 1 , } atop { 5x+y+ 2sqrt{5x+y}sqrt{5x-y} +5x-y}= 16 ; }} right. left { {{ frac{y}{x} - 4 +frac{4x}{y} = 1 , } atop { 2sqrt{(5x)^2-y^2}}= 16-10x ; }} right.$
$left { {{ frac{y^2-5xy+4x^2}{xy}=0 , } atop { (2sqrt{25x^2-y^2}})^2= (16-10x)^2 ; }} right. left { {{ y^2-5xy+4x^2=0 , } atop { 100x^2-4y^2= 256-320x+100x^2 ; }} right.$
$left { {{ y^2-5xy+4x^2=0 , } atop { y^2-80x+64=0 ; }} right. \ y^2-2cdot frac{5}{2}xy+ frac{25}{4}x^2- frac{9}{4} x^2=0,\ (y- frac{5}{2} x)^2-( frac{3}{2} x)^2=0, \ (y- frac{5}{2} x- frac{3}{2} x)(y- frac{5}{2} x + frac{3}{2} x)=0, \ (y-4x)(y-x)=0, \ left [ {{y=4x,} atop {y=x;}} right. \ 16x^2-80x+64=0, \ x^2-5x+4=0, \ x_1=1, x_2=4, \ x^2-80x+64=0, \ D_{/4}=1600-64=1536, \ x_3=20-8 sqrt{6} , x_4=20+8 sqrt{6} ;$
$y_1=4, y_2=16, y_3=20-8 sqrt{6} , y_4=20+8 sqrt{6};$