Question

if 3x-1/3x=27 then (x-1/x)^3​

Answer 1

Given :

The linear equation as

3 x - $\dfrac{1}{3x}$ = 27

To Find :

The value of ( x - $\dfrac{1}{x}$ )³

Solution :

According to question

∵    3 x - $\dfrac{1}{3x}$  = 27

Or, taking LCM

  $\dfrac{9x^{2} -1}{3x}$ = 27

Or, 9 x² - 1 = 27 × 3 x

Or,   9 x² - 81 x - 1 = 0

Solving this quadratic equation

x = $\dfrac{81\pm \sqrt{(-81)^{2}-4\times 9\times (-1)}}{2 \times 9}$

So,  x = 9

∴ The value of  $\dfrac{1}{x}$ = $\dfrac{1}{9}$

Now,

( x - $\dfrac{1}{x}$ )³  =  ( 9 - $\dfrac{1}{9}$ ) ³

              = ( $\dfrac{81-1}{9}$ ) ³

              =  ( $\dfrac{80}{9}$ ) ³

              = ( 8.89 )³

∴  ( x - $\dfrac{1}{x}$ )³  = = 702.5

Hence, The value of given expression ( x - $\dfrac{1}{x}$ )³  is 702.5   Answer