Question

x+1/x=3
x^3+1/x^3=????

Answer 1

(x+1/x)2=x2+1/x2+2x/x
32=x2+1/x2+2
9-2=x2+1/x2
x2+1/x2=7
putting the value of x2+1/x2 and x+1/x in equation 1,we get
x3+1/x3=(3)(7-1)
=3*6
=18 ----------- ANS

Answer 2

x+1/x  = 3

cube on both sides,

==========================================================

By formula,(a+b)^3 = a^3 +b^3 +3ab(a+b)

(x+1/x)^3 = 3^3

x^3 +1/x^3 +3(x*1/x)[x+1/x] = 27

x^3 +1/x^3 + 3(3) = 27

x^3 +1/x^3 + 9 = 27

x^3 + 1/x^3 = 27-9

x^3 + 1/x^3 = 18



 i hope this will help you


-by ABHAY