Question

Помогите пожалуйста
x*x+y*y=10
xy=3
это система

Answer 1

$left { {{ x^{2} + y^{2}=10 } atop {xy=3}} right. \ left { {{ x^{2} + y^{2}=10 } atop {x= frac{3}{y} }} right. \ ( frac{3}{y} )^{2} + y^{2} =10 \ frac{9}{ y^{2} } + y^{2} =10 \ frac{9+ y^{4} }{y ^{2} } = frac{10 y^{2} }{ y^{2} } \ 9+ y^{4}-10 y^{2} =0 \ y^{2} =a \ a ^{2} -10a+9=0 \ D=10 ^{2} -4*9*1=64 \ a_{1} = frac{10-8}{2} =1 \ a_{2} = frac{10+8}{2} =9 \ y^{2} =1 \ y_{1} =1 \ y_{2} =-1 \ y^{2} =9 \ y_{3} =3 \ y_{4} =-3$ $\ x_{1} =3 \ x_{2} =-3 \ x_{3} =1 \ x_{4=-1}$