Решите систему неравенств {2(x+y)=46 {x^2+y^2=17^2

Question

Решите систему неравенств
{2(x+y)=46
{x^2+y^2=17^2

Answer 1

X+y=23
x^2+y^2=289
x=(23-y)
(23-y)^2+y^2=289
529-46y+y^2+y^2=289
2y^2-46y+240=0|:2
y^2-23y+120=0
По теореме Вието
y1+y2=-p=-(-23)=23
y1*y2=q=120
y1=15
y2=8
x1=23-y1=23-15
x1=8
x2=23-y2=23-8
x2=15
(8;15) и (15;8)