SOLUTION: if (x+(1/x))=4 then find value of (x^3+(1/x^3))

Algebra ->  Linear-equations -> SOLUTION: if (x+(1/x))=4 then find value of (x^3+(1/x^3))      Log On


   

Question 763381: if (x+(1/x))=4 then find value of (x^3+(1/x^3))
Answer by ramkikk66(644) About Me  (Show Source):
You can put this solution on YOUR website!
This is very similar to question 763384, which has been solved.
We will use the identity
%28a+%2B+b%29%5E3+=+a%5E3+%2B+b%5E3+%2B+3%2Aa%2Ab%28a+%2B+b%29 ------- (1)
x+%2B+1%2Fx+=+4
%28x+%2B+1%2Fx%29%5E3+=+4%5E3+=+64
But by the identity (1),
%28x+%2B++1%2Fx%29%5E3+=+x%5E3+%2B+1%2Fx%5E3+%2B+3%2Ax%2A%281%2Fx%29%2A%28x+%2B+1%2Fx%29 ------- (2)
Substituting for (x + 1/x) as 4
%28x+%2B+1%2Fx%29%5E3+=+x%5E3+%2B+1%2Fx%5E3+%2B+3%2A1%2A4 ------- (3) ---> x*1/x = 1
64+=+x%5E3+%2B+1%2Fx%5E3+%2B+12 ------ (4)
So,
x%5E3+%2B+1%2Fx%5E3+=+64+-+12+=+52
:)