Question

Решите уравнение: (x+2)^3-(x-2)^3=2x(6x+2)

Answer 1

Ответ:

x = 4

Объяснение:

(x + 2)³ -(x - 2)³ = 2x × (6x + 2)

x³ + 6x² + 12x + 8 - (x³ - 6x² + 12x - 8) = 12x² + 4x

x³ + 6x² + 12x + 8 - x³ + 6x² - 12x + 8 = 12x² + 4x

12x² + 16 = 12x² + 4x

16 = 4x

4x = 16

x = 4

Answer 2

$(x+2)^3-(x-2)^3=2x(6x+2)\\\\\star \; \; A^3-B^3=(A-B)(A^2+AB+B^2)\; \; \star \\\\\Big ((x+2)-(x-2)\Big )\Big ((x+2)^2+(x+2)(x-2)+(x-2)^2\Big )=12x^2+4x\\\\4\cdot \Big ((x^2+4x+4)+(x^2-4)+(x^2-4x+4)\Big )=12x^2+4x\; |:4\\\\3x^2+4=3x^2+x\\\\x=4$