SOLUTION: if (x-(1/x))=3 find the value of (x^3-(1/x^3))

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Question 763384: if (x-(1/x))=3 find the value of (x^3-(1/x^3))
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
We will use the identity
%28a+-+b%29%5E3+=+a%5E3+-+b%5E3+-+3%2Aa%2Ab%28a+-+b%29 ------- (1)
x+-+1%2Fx+=+3
%28x+-+1%2Fx%29%5E3+=+3%5E3+=+27
But by the identity (1),
%28x+-+1%2Fx%29%5E3+=+x%5E3+-+1%2Fx%5E3+-+3%2Ax%2A%281%2Fx%29%2A%28x+-+1%2Fx%29 ------- (2)
Substituting for (x - 1/x) as 3
%28x+-+1%2Fx%29%5E3+=+x%5E3+-+1%2Fx%5E3+-+3%2A1%2A3 ------- (3) ---> x*1/x = 1
27+=+x%5E3+-+1%2Fx%5E3+-+9 ------ (4)
So,
x%5E3+-+1%2Fx%5E3+=+36
:)