Question

Hallar el conjunto solución en R:
x(x+2)(x+4)+x^3=2〖(x+1)〗^3

Answer 1

Explicación paso a paso:

$x(x + 2)(x + 4) + {x}^{3} = 2( {x + 1)}^{3} \\ ( {x}^{2} + 2x)(x + 4) + {x}^{3} = 2( {x}^{3} + 3 {x}^{2} + 3x + 1) \\ {x}^{3} + 4 {x}^{2} + 2 {x}^{2} + 8x + {x}^{3} = 2 {x}^{3} + 6 {x}^{2} + 6x + 2 \\ 2 {x}^{3} + 6 {x}^{2} + 8x = 2 {x}^{3} + 6 {x}^{2} + 6x + 2 \\ 2 {x}^{3} + 6 {x}^{2} + 8x - 2 {x}^{3} - 6 {x}^{2} - 6x - 2 = 0 \\ 2x - 2 = 0 \\ 2x = 2 \\ x = \frac{2}{2} = 1 \\ x = 1$