MathDB

8

Part of 2019 New Zealand MO

Problems(1)

\prod_{i=1}^{X_n} \frac{x_i}{s + 1 - x_i} + \prod_{i=1}^{Y_n} (1 - x_i) \le 1

Source: New Zealand MO 2019 Round 1 p8

9/20/2021
Suppose that x1,x2,x3,...xnx_1, x_2, x_3, . . . x_n are real numbers between 00 and 1 1 with sum ss. Prove that ∏i=1nxis+1−xi+∏i=1n(1−xi)≤1.\prod_{i=1}^{n} \frac{x_i}{s + 1 - x_i} + \prod_{i=1}^{n} (1 - x_i) \le 1.
algebrainequalities