Browse · MATH Print → jmc algebra junior Problem Let 0≤a≤1 and 0≤b≤1. Find the largest possible value of ab+1a+b. Solution — click to reveal Since 0≤a≤1 and 0≤b≤1, (1−a)(1−b)≥0.Then 1−a−b+ab≥0, so a+b≤ab+1. Hence, ab+1a+b≤1.Equality occurs when a=b=1, so the maximum value is 1. Final answer 1 ← Previous problem Next problem →