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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

User Ido Sela
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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

User Nealon
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