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  • Użytkownik Zadane
2009-09-08T19:26:15+02:00
A) x² - 4x + y=0
x(x-4) - y = 0

y=-x²+4x
x²-4x-(-x²+4x)=0

y=-x²+4x
x²-4x+x²-4x=0

y=-x²+4x
2x²-8x=0

delta=64-4*2*0=64
√Δ=8
x1=8-8/4=0
x2=8+8/4=16/4=4

y1=0
y2=16+16=32

b) x² + y² + 2x + 6y - 6 = 0
x = -5

25+ y²-10+6y-6=0
x = -5

y²+6y-16=0
Δ=36-4*1*(-16)=36+64=100
√Δ=10
x1=-6-10/2=-16/2=-8
x2=-6+10/2=4/2=2

y1=0
y2=0

c) xy = -1
2x + y = 1

xy = -1
y = 1-2x

(1-2x)x=-1
y = 1-2x

x-2x²=-1
-2x²+x+1=0
Δ=1-4*(-2)*1=1+8=9
√Δ=3
x1=-1-3/-4=-4/-4=1
x2=-1+3/-4=2/-4=-1/2

y1=1-2*1=1-2=-1
y2=1-2*(-1/2)=1+1=2