Question

Let a,b,c and x elements in the group G. In each of the following solve for x in terms of a,b, and c.

solve simultaneously x^2 =a and x^5 = e

Answer 1

Every
`g\in G` has an inverse
`g^(-1)\in G` such that
`gg^(-1)=g^(-1)g=e`. So

`x^5=x^2x^2x=e\implies a^2x=e\implies x=(a^(-1))^2`