Question

Решите систему уравнений

$left { {{x^{2}+y^{2}=25} atop {x+y=7}} right.$

Answer 1

$x^{2} +y ^{2} =25 \ x+y=7 \ \ y=7-x \ \ x^{2} +(7-x) ^{2} =25 \ x^{2} +49+x^{2} -14x-25=0 \ 2 x^{2} -14x+24=0|:2 \ x^{2} -7x+12=0 \ D=49-4*12=49-48=1 \ sqrt{D} =1$

$x_{1} = frac{7+1}{2} = frac{8}{2} =4 \ x_{2} = frac{7-1}{2} = frac{6}{2} =3 \ \ y_{1} =7-4=3 \ y _{2} =7-3=4 \ \ \ left { {{y=3} atop {x=4}} right. left { {{4=2} atop {x=3}} right.$