given that x+1/x=3
(a) expand (x+1/x)^3 and use your expansion to show that x^3+1/x^3=18.
(ii) expand (x+1/x)^5, using your expansion and the previous results to find the value of x^5+1/x^5
(x+1/x)^3 = x^3 + 3x + 3/x + 1/x^3
= x^3+1/x^3 + 3(x+1/x)
so
27 = x^3+1/x^3 + 3*3
18 = x^3+1/x^3
do likewise for (ii)