Решите уравнение: x² - 1/2 x = 1/2. Created by haka228. algebra-ru

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ShirokovP

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X^2 - 1/2x - 1/2 = 0 /*2
2x^2 - x - 1 = 0
D = 1 + 4*2 = 9
x1 = (1 + 3)/4 = 4 /4 = 1
x2 = ( 1 - 3)/4 = - 2/4 = - 1/2

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haka228 Что за D такое?

koingrel D - дискриминант.

haka228 Да блин, я то в 7 классе учусь

koingrel Хорошо, сейчас в своем ответе покажу как не через дискриминант.

koingrel

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Х^2 - 1/2х = 1/2 |*2
Умножаем все на два:
2х^2 - х = 1
2х^2 - х - 1 = 0
Первый способ:
D = (-1)^2 - 4*2*(-1) = 1 + 8 = 9 = 3^2
x = (1 +- v9)/4

x1 = (1 + v9)/4 = (1 + 3)/4 = 4/4 = 1
x2 = (1 + v9)/4 = (1-3)/4 = -2/4 = -1/2
ОТВЕТ: х1 = 1; х2 = -1/2
ПРИМЕЧАНИЕ: v - корень
Второй способ:
2х^2 - x - 1 = 0
(2x + 1)*(x - 1) = 0
2x + 1 = 0 или х+1 = 0
2х = -1 ; х2 = -1
х1 = -1/2 ; x2 = -1

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