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Rozwiąż równania kwadratowe

a) 6x^2 + 7x + 2 = (2 - 3x) (3x + 2)
b) 1/2x^2 - 3x + 9 = (x - 3) (x - 5)


Odpowiedź :

Szczegółowe wyjaśnienie:

6x²+7x+2 = (2-3x)(3x+2)

6x²+7x+2 = 4-9x²

15x²+7x-2 = 0

∆= 7²-4*15*(-2)

∆= 49+120

∆= 169

√∆ = 13

x1 = (-7-13)/(2*15) = -20/30 = -2/3

x2 =(-7+13)/(2*15) = 6/30 = 1/5

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1/2 x²-3x+9 =(x-3)(x-5)

1/2 x²- 3x+9 = x²-8x+15

-1/2 x² +5x -6 =0 |* (-2)

x²-10x+12 =0

∆ = (-10)² -4*1*12

∆ = 100-48

∆ = 52

√∆ = √52 = 2√13

x1 = (10-2√13)/2 = 5-√13

x2 = (10+2√13)/2 = 5+√13

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