Question

C) Hence solve (1+2x)³+(1-2x)³=8​

Answer 1

Answer:

$x = \frac{1}{2}$

Step-by-step explanation:

Apply Sum of Cubes

$(1 + 2x) {}^{3} + (1 - 2x) {}^{3} = ((1 + 2x + (1 - 2x)( {(1 + 2x)}^{2} - (1 + 2x)(1 - 2x) + {(1 - 2x)}^{2}$

Simplify

$= (2)((4 {x}^{2} + 4x + 1) -( - 4 {x}^{2} + 1) + ( {4x}^{2} - 4x + 1)$

Simplify

$(2)(12 {x}^{2} + 1) = 8$

$24 {x}^{2} + 2 = 8$

$24 {x}^{2} = 6$

${x}^{2} = \frac{1}{4}$

$x = \frac{1}{2}$