Question

При каких значениях ,а разность корней уравнения ах²+х-2=0 равна 3?

Answer 1

D = B^2 - 4ac = 1 - 4 * (-2)*a = 1+8a

X1 = (-B+D^(1/2))/2a

X2 = (-B-D^(1/2))/2a

X2 - X1 = 3

((-B+D^(1/2))-(-B-D^(1/2)))/2a

(2*D^(1/2))/2a = 3
(2*(1+8a)^(1/2))/2a = 3
(1+8a)^1/2 = 3a
ОДЗ a>= -0.125
Возводим в квадрат
1+8a = 9a^2
9a^2-8a-1 = 0
D = 64 - 4*(-1)*9 = 64+36 = 100

A1 = (8+10)/18 = 1
A2 = (8-10)/18 = -1/9