Դաս. 11

Վարժ. 226
ա) x^3 + 5x^2 + 6x = 0 [x = 0
x (X62 + 5x + 6) = 0 =>[x^2 + 5x + 6 = 0 (1)
x^2 + 5x + 6 = 0
D = 25 — 4 * 6 * 1 = 1
[x = -5-1/2 = -3
[x = -5+1/2 = -2
(1) => [x = 0 [ x = -2 [x = -2
բ) x^3 = 4x^2 + 3x = 0 [x = 0
x(x^2 — 4x + 3) = 0 => [x^2-4x+3 = 0 (1)
x^2 — 4x + 3 =0
D = 16 — 4 *1 * 3 = 16 — 12 = 4
[x = 4-2/2 = 2/2 1
[x = 4+2/2 = 6/2 = 3
(1) => [x = 0 [x = 1 [x = 3
գ)x^4 = 2x^3 + 3x^ 2
x^4 — 2x^3 — 3x^2 = 0 [x^2 = 0 (1)
x^2(x^2 — 2x — 3) = 0 > [x^2 — 2x — 3 = 0
x^2 — 3x — 3 = 0
D = 4 + 12 = 16
[x = 2 — 4/2 = -1 [x = 0
[x = 2 + 4/2 = 3 (1) > [x = -1
Պատ.՝ 0;-1;3 [x = 3
ը)(x — 3)^2 x = 0 >[(x-3)^2 = 0>[x-3=0>x=3
Պատ.՝ 0;3 [x = 0 > [x = 0 > [x = 0
զ) x^3 + x = 2x^2
x^3 — 2x^2 + x = 0 [x = 0 (1)
x (x^2 — 2x + 1) = 0 > [x^2 — 2x + 1 = 0
x^2 — 2x + 1
D = 4 — 4 * 1 * 1 = 4 — 4 = 0 [x = 0
X = 2/2 = 1 (1) > [x = 1 Պատ.՝ 0;1