MathCastle
Groups and FieldsChallengeGroups and the Group Axioms

Groups and the Group Axioms · Challenge problem

On Q∖{−1}\mathbb Q\setminus\{-1\} the operation a∗b=a+b+aba*b=a+b+ab makes a group. Find the sum of all xx in this group with x∗x=8x*x=8.