Applications of Inequality - RMS, AM, GM, HM | Core Concepts & Tricks | Jee Mains | Advanced

Hello Guys, today we are going to explain applications of Famous inequality RMS greater than equal to AM greater than equal to GM greater than equal to HM. Its applications are used in Algebra, Trigonometry and calculus branch of mathematics. The relation can be proved mathematically and geometrically as well. Skipping the unnecessary proofs we are moving straight forward the application of the results from Jee Mains and advanced perspective.
At first, we have explained the terms root mean square(RMS), arithmetic mean (AM), Geometric Mean (GM) and harmonic Mean (HM). The most important thing in the inequality is that the equality holds only and only if all the numbers are equal.
We are going to drive a result using the inequality AM greater than equal to GM which is mostly used inequality in problems. According to the derived result sum of a number with its reciprocal is always greater than or equal to if the number is positive and the sum is greater than or equal to 2 if the number is negative and the sum is less than or equal to -2 if the number is negative.
using the obtained result we have discussed a problem of calculus which involves the concept of range of functions.
Later in the video lecture we have discussed plenty of examples keeping the important things in mind that while using the inequality we should always check for the equality conditions
We have discussed the applications of the result in trigonometry branch of mathematics also.

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Team IITian explains