Question

Решите систему уравнений а)x+y=10 x^2-y^2=40 б)x-y=4 x^2-y^2=40 в)x-y=4 xy=5 г)x-y=4 xy=12

Answer 1

а)x+y=10
x^2-y^2=40

x=10-y
(10-y)^2 -y^2=40
100-20y+y^2-y^2=40
-20y=-60
y=3
x=7

б)x-y=4
x^2-y^2=40

x=4+y
(4+y)^2-y^2=40
16+8y+y^2-y^2=40
8y=24
y=3
x=7

в)x-y=4 xy=5
x=4+y
y(4+y)=5
y^2+4y-5=0
d=16+20=36
y1=1  x1=5
y2=-5  x2=-1

г)x-y=4
xy=12
x=4+y
y(4+y)=12
y^2+4y-12=0
d=16+48=64
y1=2 x1=6
y2=-6 x2=-2