1)(х+1)³-(х-1)³=х(6х+2) 2)(x-2)³-3x²-4=(x-3)³ 3)(x+2)³-(x-1)³=9x²+36 - вопрос №345092111162223433219364 от kat2000T 29.06.2021 08:33

Question

Алгебра: 1)(х+1)³-(х-1)³=х(6х+2) 2)(x-2)³-3x²-4=(x-3)³ 3)(x+2)³-(x-1)³=9x²+36 4)(x+3)³=x²(x+9)

kat2000T · Answer

№1
x ^3 - 3x^2 + 3x - 1 - (x^3 -3x^2 + 3x - 1) = 6x^2 + 2x
   6x^2 + 2x = 0
   2x (3x + 1) = 0
    2x = 0
   x1 = 0
3x + 1 = 0
3x = - 1
   x2 = - 1/3

№3
x^3 + 3x^2*2 + 3x*4 + 8 - ( x^3 - 3x^2 + 3x -1) = 9x^2 + 36
x*3 + 6x^2 + 12x + 8 - x^3 + 3x^2 - 3x + 1) = 9x^2 + 36
x^3 + 6x^2 - 9x^2 + 12x + 8 - 36 -x^3 + 3x^2 - 3x + 1 = 0
12x - 3x -28 + 1 = 0
9x = 28 - 1
9x = 27
x = 3

№4
x^3 + 9x^2 + 27x + 27 - x^3 - 9x^2 = 0
27x = - 27
    x = - 1

№2
х^3 - 6x^2 +12x - 8 -3x^2 -4 = x^3 - 9x^2 + 27x - 27
x^3 - 6x^2 + 12x - 8 - 3x^2 -4 - x^3 + 9x^2 - 27x + 27 = 0
12x - 12 - 27x + 27 = 0
- 15x = -27 + 12
- 15x = - 15
   x = 1