Question

Given real numbers a, b, c, d, e > 1 Prove that

a²/c - 1 + b²/b - c²/e - 1 + d²/a - 1 + e²/b - 1 ≥ 20.

Answer 1

Not that (a - 2)² ≥ 0 and a² ≥ 4(a - 1). since a > 1 we have a²/a - 1 ≥ 4

By applying AM-GM inequality we get