Question

If x-1/x=3 find x^3-1/x^3
anyone find plz.......

Answer 1

Heya !!

X - 1/X = 3

Cubing on both sides ,

( X - 1/X)³ = (3)³

We know that,

( a - b )³ = a³ - b³ - 3ab × ( a - b ).

So,

( x - 1/x)³

=> X³ - 1/X³ - 3X × 1/X × ( X - 1/X) = 27

=> X³ - 1/X³ - 3 × 3 = 27

=> X³ - 1/X³ - 9 = 27

=> X³ - 1/X³ = 27 + 9

=> X³ - 1/X³ = 36.

Answer 2

X^3 - Y^3 = (X-Y) (X^2 + Y^2 + XY)
SO
X^3 - 1/X^3 = (x-1/x)(x^2 + 1/x^2 + x*1/x)
NOW
(X-1/X)^2 = X^2 + 1/X^2 - 2*X*1/X
3^2 = X^2 + 1/X^2 - 2
X^2 + 1/X^2 = 9+2 = 11
NOW PUT ALL THE VALUES OF GIVEN EQUATION WE GET
X^3 - 1/X^3 = 3*(11+1) = 3*12 = 36