Find the following

Question

If [a - 1/a ] = 3 then a^3 - 1/a^3 = ?

Answer 1

The general rule is

x³-y³=(x-y)(x²+xy+y²)

Rearrange a³-(1/a³) to be (a)³-(1/a)³

Then x=a and y=1/a in the general rule

(a-1/a)(a²+(a)(1/a)+(1/a²))

Since (a-1/a)=3

3(a²+1+(1/a²))