Question

Решите.......................

Answer 1

$left { {{ sqrt{x} + sqrt{y} =5} atop {x+y=13}} right. \ left { {{( sqrt{x} + sqrt{y})^2=5^2} atop {x=13-y}} right. \ x+y+2 sqrt{xy} =25 \ 13+2 sqrt{xy} =25 \ 2 sqrt{xy} =12 \ sqrt{xy} =6 \ xy=36 \ (13-y)y=36 \ y^2-13y+36=0 \ (y-4)(y-9)=0 \ y_1=4; x_1=13-4=9 \ y_2=9; x_2=13-9=4$
Ответ: (4; 9); (9; 4)

$sqrt{x+2} =2+ sqrt{x-6} (x geq 6) \ ( sqrt{x+2})^2 =(2+ sqrt{x-6})^2 \ x+2=4+x-6+4 sqrt{x-6} \ 4=4 sqrt{x-6} \ 1= sqrt{x-6} \ x-6=1 \ x=7$
Ответ: 7

Answer 2

спасибо