Answer:
[tex]x = \frac{1}{2} [/tex]
Step-by-step explanation:
Apply Sum of Cubes
[tex](1 + 2x) {}^{3} + (1 - 2x) {}^{3} = ((1 + 2x + (1 - 2x)( {(1 + 2x)}^{2} - (1 + 2x)(1 - 2x) + {(1 - 2x)}^{2} [/tex]
Simplify
[tex] = (2)((4 {x}^{2} + 4x + 1) -( - 4 {x}^{2} + 1) + ( {4x}^{2} - 4x + 1)[/tex]
Simplify
[tex](2)(12 {x}^{2} + 1) = 8[/tex]
[tex]24 {x}^{2} + 2 = 8[/tex]
[tex]24 {x}^{2} = 6[/tex]
[tex] {x}^{2} = \frac{1}{4} [/tex]
[tex]x = \frac{1}{2} [/tex]
