Question

Решите систему уравнений х+у=1 х^2+у^2=25

Answer 1

х+у=1⇒x=1-y
х^2+у^2=25
1-2y+y²+y²-25=0
2y²-2y-24=0
y²-y-12=0
y1+y2=1 U y1*y2=-12
y1=-3⇒x1=1+3=4
y2=4⇒x2=1-4=-3
(4;-3);(-3;4)

Answer 2

$\left \{ {{x+y=1 } \atop {x^2+y^2=25 }} \right. \\ \\ \left \{ {{y=1-x } \atop {x^2+(1-x)^2=25 }} \right. \\ \\ \left \{ {{y=1-x } \atop {x^2+1-2x+x^2=25 }} \right. \\ \\ \left \{ {{y=1-x } \atop {2x^2-2x-24=0 }} \right. \\ \\ \left \{ {{y=1-x } \atop {x^2-x-12=0 }} \right.$
Решаем второе уравнение
х²-х-12=0
D=(-1)²-4·(-12)=1+48=49=7²
x₁=(1-7)/2=-3           или    х₂=(1+7)/2=4
у₁=1-х₁=1-(-3)=4              у₂=1-х₂=1-4=-3
ответ. (-3;4)      (4;-3)