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Given a, b, c ∈ G, solve for x (show all your steps): 1. {(x∗a∗x)∗(x∗a∗x)∗(x∗a∗x)=b∗x and...

Given a, b, c ∈ G, solve for x (show all your steps):

1. {(x∗a∗x)∗(x∗a∗x)∗(x∗a∗x)=b∗x and x∗x∗a=(x∗a)^−1}

2. x∗x∗b = x∗a−1∗c

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Answer #1

In the group , and .

Now, left hand side is . So . Then .

. Then . Then relation between a,b,c must be . So we are done.

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