Question

Find the value ofx^3-(1/x^3) when x-(1/x)=a​

Answer 1

Answer:

Step-by-step explanation:

X^3 – 1/x^3  =?

So using here (a – b)^3  = a^3  - b^3 -3a^2 b -3ab^2

(x-1/x)^3  = x^3 – 1/x^3  - 3(x)^2 1/x – 3x(1/x)^2

(x-1/x)^3  = x^3 – 1/x^3  - 3(x)^2 1/x – 3x1/x^2

(x-1/x)^3  = x^3 – 1/x^3  - 3x( 1) – 3(1/x) ………………. @

We know value of x-1/x=a

So , from step @  

(a)^3  = x^3 – 1/x^3  - 3x – 3(1/x)

(a)^3  = x^3 – 1/x^3  - 3(x-1/x)……………(taking 3 common)

(a)^3  = x^3 – 1/x^3  - 3a

(a)^3 +3a = x^3 – 1/x^3  

So x^3 – 1/x^3  = (a)^3 +3a