Question

if x- 1 /x =5 then, find the value of x^3-1/x^3.

Answer 1

Hi ...dear
here is your answer!!
Given,
x- 1 /x =5.
Making cube of both sides!!
See picture!!!
Hope it helped you!!
Regards Brainly Star Community
#shubhendu!!

Answer 2

The simplified form of the given equation is 140.

Solution:

The first equation given,

$x-\frac{1}{x}=5$ …….. (i)

If we do the cube of equation (i) we get,

$\left(x-\frac{1}{x}\right)^{3}=5^{3}$

$x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times x \times\left(\frac{1}{x}\right) \times\left(x-\frac{1}{x}\right)=125$

$x^{3}-\left(\frac{1}{x}\right)^{3}-3\times(x-\frac{1}{x})=125$

$x^{3}-\left(\frac{1}{x}\right)^{3}-3 \times 5=125$

Grouping the terms,

$x^{3}-\left(\frac{1}{x}\right)^{3}=125+15$

$x^{3}-\left(\frac{1}{x}\right)^{3}=140$