Դաս. 11

Վարժ. 223
ա) a 8 b = 0 => [a = 0 [b = 0
բ) ճիշտ է
գ) x^2-x = 0
x(x-1) = 0=> [x=0 [x-1=0 => [x=0 [x=1
x -1 = 0 => x = 1
Պատ.՝ համարժեք չէ
դ) Հավասարմմար արմատ է:
Վարժ.224
ա) (x-1)(x-2) = 0=> [x-1 = 0[x-2 = 0 => [x = 1 [x = 2
Պատ.՝ 1;2
բ) (x-3)(x+4) = 0 => [x-3 =0 [x+4 = 0 => [x = 3 [ x = -4
Պատ.՝ 3; -4
գ) (x-7)^2 = 0 => x — 7 = 0 => x = 7
Պատ.՝ 7
դ) (x+4)(x-6) = 0 => [x +4 = 0 [x — 6 =0 => [x = -4 [ x= 6
Պատ.՝ -4; 6
ե) x (x — 2) = 0 => [x = 0 [ x — 2 = 0 => [x = 0 [x = 2
Պատ.՝ 0; 2
զ) (x+3) x = 0 => [x + 3 = 0 [x = 0 => [x = -3 [x = 0
Պատ.՝ -3; 0
է) 3x^2 = 0 => x^2 = 0 => x = 0
Պատ.՝ 3; 0
ը)-x^2 (3+x) = 0 => [-x^2 = 0 [3+x = 0 => [x^2 = 0 [x = -3 => [x = 0 [x = -3
Պատ.՝ 0; -3
Վարժ. 225
ա) 2x^2 = 3x = 0 => [x (2x — 3) = 0 => [x = 0 [2x-3 = 0 => [x = 0 [2x = 3 => [x = 0 [ x = 3/2
Պատ.՝ 0; 3/2
բ) 7x^2 + 5x = 0 => x (7x + 5) = 0 => [x = 0 [7x + 5 = 0 => [x = 0 [7x = -5 => [x = 0 [x = -5/7
Պատ.՝ 0; -5/7
դ) 1 — x^3 = 0 => x(1-x^2) = 0 => x^2 = 0 => x = 0
Պատ.՝ 1;0
զ) x^3 — 8 = 0 => x^2 = 0 => x = 0
Պատ.՝ 0; 8
է) 125 — x^3 = 0
x (125 — x^2) = 0 => x^2 = 0 => x = 0
Պատ.՝ 125; 0
Վարժ. 227
ա) (3x + 3)(2x + 5) = 0=> [3x+3 = 0 [2x+5 = 0=> [3x = -3 [ 2x = -5 => [x = -1 [ x = -5/2
Պատ.՝ -1/ -5/2
բ) (x^2 + 2x + 1) (x^2 — 5x + 7) = 0 => [x^2 + 2x + 1 = 0 [x^2 = 5x+ 7 = 0 (1)
x^2 + 2x +1 = 0
D=4-4*1*1=0
x=-2/2=-1
x^2-5x+7=0
D=25-4*1*7=25-28=-3 չի լուծվում
(1)=>[x=-1
Պատ.՝ -1
գ) (5-x)(3x+2) = 0 => [5-x=0 [3x+2 = 0 => [-x = -5 [ 3x = -2 => [x=5 [ x = -2/3
Պատ.՝ 5; -2/3
զ) (x^2-5x+6)(3x-2)=0=>[x^2-5x+6=0 [3x-2=0=>[x^2-5x+6=0 [3x=2 => [x^2-5x+6=0 [x=2/3 (1)
x^2-5x+6=0
D=25-4*1*6=25-24=1
[x=5-1/2=4/2=2
[x=5+1/2=6/2=3
(1)=>[x=2/3 [x=2 [x=3
Պատ.՝ 2/3;2;3
ը) (x^2-1) (x^2 0 5x + 6) = 0 => [x^2 — 1 = 0 [x^2 — 5x + 6 = 0 (1)
x^2 — 1 = 0 => x^2 = 1 => [x=1 [x = -1
x^2 — 5x + 6 = 0
D = 25 — 4 *1 * 6 = 25 — 24 = 1
[x = 5 — 1/2 = 4/2 = 2
[x = 5 + 1/2 = 6/2 = 3
(1) = [x = 1 [x = -1 [x = 2 [x = 3
խ) (x^2 + 1)(x^2 — 2x+ 7) = 0=> [x^2 + 1 = 0 [x^2 — 2x + 7 = 0 (1)
x^2 +1 = 0 => x^2 = -1 չի լուծվում
x^2 — 2x + 7 = 0
D = 4 — 4 *1 * 7 = 4 — 28 = -24 չի լուծվում