Решите номер.Есть вложение.

$\left \{ {{x^2+y^2=37} \atop {xy=6}} \right. \\\ x= \frac{6}{y} \\\ ( \frac{6}{y} )^2+y^2=37 \\\ \frac{36}{y^2}+y^2=37 \\\ 36+y^4=37y^2 \\\ y^4-37y^2+36=0 \\\ y^4-y^2-36y^2+36=0 \\\ y^2(y^2-1)-36(y^2-1)=0 \\\ (y^2-1)(y^2-36)=0 \\\ y^2=1; \ y_1=1; \ y_2=-1 \\\ y^2=36; \ y_3=6; \ y_4=-6 \\\ x_1= \frac{6}{1} =6; \ x_2= \frac{6}{-1} =-6 \\\ x_3= \frac{6}{6} =1; \ x_4= \frac{6}{-6} =-1$
Ответ: (6; 1); (-6; -1); (1; 6); (-1; -6)