Question

Решите номер.Есть вложение.

Answer 1

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