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2010-03-10T09:47:54+01:00
A) (x-3)² = 25
x²-6x+9=25
x²-6x+9-25=0
x²-6x-16=0
∆= b²-4ac
∆=(-6) ²-4x1x(-16)
∆=36+64
∆=100
√∆=10
-b+ √∆ 6+10 16
x1=---------=--------=----=8
2a 2x1 2

-b+ √∆ 6-10 -4
x2=---------=--------=----=-2
2a 2x1 2



b)4(3x+2)² = 8
4(9 x²+12x+4)=8
36x²+48x+16=8
36x²+48x+16-8=0
36x²+48x+8=0
∆= b²-4ac
∆=48²-4x36x8
∆=2304-1152
∆=1152
-b+ √∆ -48+1152 1104
x1=---------=-------------=--------=15 24/72
2a 2x36 72

-b+ √∆ -48-1152 -1200
x2=---------=------------=---------=-16 48/72
2a 2x36 72

c) ⅓ (6-5x) ² = 0
⅓(36-60x+25x²)=0
12-20x+25/3 x²=0
25/3 x²-20x+12=0
∆= b²-4ac
∆=(-20)²-4x(25/3)x12
∆=400-400
∆=0

-b 20 20
x1= x2=-------=---------=----=20x3/50=6/5
2a 2x25/3 50/3


d) (0,2x-3)² = -1,4
0,04x²-1,2x+9=1,4
0,04x²-1,2x+9-1,4=0
0,04x²-1,2x+7,6=0
4/100 x²-12/10x+76/10=0/ to mnoży przez100
4 x²-120x+760=0
∆= b²-4ac
∆=(-120)²-4x4x760
∆=14400-12160
∆=2240
-b+ √∆ 120+2240 2360
x1=---------=-------------=--------=295
2a 2x4 8

-b+ √∆ 120-2240 -2120
x2=---------=------------=---------=-265
2a 2x4 8
e) -3(5x+½)² = 2
-3(25x²+5x+1/4)=2
-75 x²-15x-3/4=2 /to mnożymy x4
-300 x²-60x-3=8
-300 x²-60x-3-8=0
-300 x²-60x-11=0
∆= b²-4ac
∆=(-60)²-4x(-300)x(-11)
∆=3600-13200
∆=-9600
brak mjesc zarowych bo ∆ jest na minusie

f) -0,3(0,7x+1)² = -6
-3/10(7/10x+1) ²=-6
-3/10(49/100x²+14/10x+1)=-6
-147/1000x²-42/100x-3/10=-6 / to mn x1000
-147x²-420x-300=-6000
-147x²-420x-300+6000=0
-147x²-420x-5700=0
∆= b²-4ac
∆=(-420)²-4x(-147)x(-5700)
∆=176400-3351600
∆=-3175200 brak miejsc zerowych

g) x²-4x+1 = 0
∆= b²-4ac
∆=(-4)²-4x1x1
∆=16-16
∆=0
-b 4 4
x1= x2=---=----=---=2
2a 2x1 2
h) x²+6x-7 = 0
∆= b²-4ac
∆=6²-4x1x(-7)
∆=36+28
∆=64
√∆=8
-b+ √∆ -6+8 2
x1=---------=--------=----=1
2a 2x1 2

-b+ √∆ -6-8 -14
x2=---------=--------=----=-7
2a 2x1 2
i) x² +3x-2,5 =
∆= b²-4ac
∆=3²-4x1x(-2,5)
∆=9+10
∆=19
-b+ √∆ -3+19 16
x1=---------=--------=----=8
2a 2x1 2

-b+ √∆ -3-19-22
x2=---------=--------=----=-11
2a 2x1 2
3 2 3