Question

if 2x+1/2x=21,then find 8x^3+1/8x^3

Answer 1

(2x) + 1/(2x) = 21
use formula,
a³ + b³ = (a + b)³ - 3ab(a + b)

(2x)³ + 1/(2x)³ = (2x + 1/2x)³ - 3(2x).1/(2x)(2x + 1/2x)
8x³ + 1/8x³ = (21)³ - 3(21) = 21(441 -3)
= 21 × 438 = 9198

Answer 2

$\text{Given,}\\\frac{2x+1}{2x}= 21\\\\We \ know,\\\boxed{\boxed{a^3 + b^3=(a+b)^3-3ab(a+b)}}\\\text{Using this,}\\\frac{(2x+1)^3}{(2x)^3}=\{ \frac{2x+1}{2x}\}^3 - \frac{3(2x)1}{2x}\left(\frac{2x+1}{2x}\right)\\\\\frac{8x^3 + 1}{8x^3}=\{21\}^3 - 3(21)\\~~~~~~~~~= 21\times438\\~~~~~~~~~=\boxed{\boxed{\bold{9198}}}$