Kvadratlikning
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- Abel
- Innlegg: 637
- Registrert: 11/11-2019 18:23
Hei,
x^2 - 1/2 x = 3
x^2 - 1/2 x + ((1/2)/2)^2 = 3 + ((1/2)/2)^2
x^2 - 1/2 x + 1/16 = 3 + 1/16
(x - 1/4)^2 = 49/16
x - 1/4 = +/- 7/4
x = 1/4 +/- 7/4
x = 2
eller
x = -3/2
Altså hovedregel:
x^2 + bx = c
x^2 + bx + (b/2)^2 = c + (b/2)^2
(x + b/2)^2 = c + (b/2)^2
x^2 - 1/2 x = 3
x^2 - 1/2 x + ((1/2)/2)^2 = 3 + ((1/2)/2)^2
x^2 - 1/2 x + 1/16 = 3 + 1/16
(x - 1/4)^2 = 49/16
x - 1/4 = +/- 7/4
x = 1/4 +/- 7/4
x = 2
eller
x = -3/2
Altså hovedregel:
x^2 + bx = c
x^2 + bx + (b/2)^2 = c + (b/2)^2
(x + b/2)^2 = c + (b/2)^2