Question

9 класс. Решить три уравнения

Answer 1

Ответ:

1) х = -2,5.

2) х1 = 0,6; x2 = -1.

3) х1 = 9; x2 = -5.

Объяснение:

1)

х/5 + х/15 = -2/3

(3*х)/(3*5) + х/15 = (5*(-2))/(5*3)

3х/15 + х/15 = -10/15

(15*3х)/15 + (15*х)/15 = (15*(-10))/15

(знаменатели сокращаются)

3х + х = -10

4х = -10

х = -10/4

х = -2,5.

2)

5х² + 2х - 3 = 0

a = 5; b = 2; c = -3.

D = b² - 4*a*c

D = 2² - 4*5*(-3) = 4 + 60 = 64.

x1,2 = (-b ± √D)/2a

x1 = (-2 + 8)/2*5 = 6/10 = 0,6.

x2 = (-2 - 8)/2*5 = -10/10 = -1.

3)

(x - 8)(x + 4) = 13

x² + 4x - 8x - 32 = 13

x² + 4x - 8x -32 - 13 = 0

x² - 4x - 45 = 0

a = 1; b = -4; c = -45.

D = b² - 4*a*c

D = (-4)² - 4*1*(-45) = 16 + 180 = 196.

x1,2 = (-b ± √D)/2a

x1 = (-(-4) + 14)/2*1 = 18/2 = 9.

x2 = (-(-4) - 14)/2*1 = -10/2 = -5.

Answer 2

1) x/5+x/15=-2/3
3x+x=-10
4x=-10
x=-5/2

2)5x^2+2x-3=0
5x^2+5x-3x-3=0
5x*(x+1)-3(x+1)=0
(x+1)*(5x-3)=0
x+1=0
5x-3=0
x=-1
x=3/5
x1=-1 , x2=3/5

3) (x-8) (x+4) = 13
x^2+4x-8x-32=13
x^2-4x-32=13
x^2-4x-32-13=0
x^2+5x-9x-45=0
x*(x+5)-9(x+5)=0
(x+5)*(x-9)=0
x+5=0
x-9=0
x=-5
x=9
x1=-5 , x2=9