Question

1. Rozwiąż układ równań:
a) x²+y²+6x-16 =0
x-2y= 0
b) x²+y²-14y+48=0
x+1=0
c) (x-2)²+y²=4
y=x
d) (x-3)²+y²=25
y-1= 0

Answer 1

A) x²+y²+6x-16 =0
x-2y= 0

x²+y²+6x-16 =0
x=2y

(2y)²+y²+6*(2y)-16=0
4y²+y²+12y-16=0
5y²+12y-16=0
delta=464

y1=(-12-2√11)/10 = (-6-√11)/5 x=(-12-2√11)/5
y2=(-6+√11)/5 x=(-12+2√11)/5


b) x²+y²-14y+48=0
x+1=0 =>x=-1

1+y²-14y+48=0
y²-14y+49=0
(y-7)²=0
y=7

c) (x-2)²+y²=4
y=x

(x-2)²+y²=4
x²-4x+4-x²-4=0
-4x=0
x=0
y=0

d) (x-3)²+y²=25
y-1= 0 => y=1

x²-6x+9+1-25=0
x²-6x-15=0
delta=96

x1=(6+4√6)/2=3+2√6
x2=(6-4√6)/2=3-2√6