Browse · MATH Print → jmc algebra intermediate Problem If a@b=a−ba3−b3, for how many real values of a does a@1=0? Solution — click to reveal We want to solve a−1a3−1=0. Then a−1(a−1)(a2+a+1)=0,so a2+a+1=0. This quadratic has no real roots, so the number of real solutions is 0. Final answer 0 ← Previous problem Next problem →