# Olympiad Corner: AM GM Inequality

Arithmetic mean is greater than or equal to Geometric mean. That is called AM – GM inequality. Here is a nice problem to show how this concept can be applied.

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## A Problem on AM GM Inequality

If a + b + c + d = 3s and all numbers are positive, show that (abcd)/81 is greater than or equal to the…

## Olympiad Corner: A Problem on Triangular Inequality

If a, b, a are the sides of a triangle with perimeter 2, show that a^2 + b^2 + c^2 + 2abc is less than…

## Olympiad Corner: A Problem On Inequalities

It is time to indulge in some Olympiad math! Let us look into one inequality problem. Do you have a mathematical question to ask? Do…

## Olympiad Corner: Summing Up A Series

We have a series: tan(1)tan(2) + tan(2)tan(3) + … + tan(2019)tan(2020). What is its value? Here is a summation problem involving trigonometric functions. Do you…

## Olympiad Corner: What Is The Sum Of The Corner Entries?

In a 4 x 4 array of 16 numbers, the sum of the numbers in each row, column, and diagonal is 1. Find the sum…