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

[IITianexplains]

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Team IITian Explains

[jamesstewart]

Thanku so much DJ sir 🙏🙏🙏
For clearing my all doubts ....
The underrated Wizard of mathematics 🙏🙏🙏

[VivekYadav-dsoz]

On solving the inequality, we can say that sin^4(x) = (b/a)^2.
Since sin^4(x) 's range lies in [0, 1]. Which implies 0 <= (b/a)^2 <= 1. => b/a = [0, 1].
This means the inequality only holds as long as b <= a.

[MDSadiq-jchb]

You are the best teacher of mathematics I had ever seen thank you sir by heart

[sahilnaik]

sir the range [2ab, infinity) will be when is it correct or and for other cases what will be the range

[rajdeepmallick]

sir bohot bariyaaa hayyyy yee video.... bohot sare questions jaldi ho sakte hayy iske 😁😁😁😁 carry on....bohot dino bad app se mulakat hi bar bar ate raheee...❤

[lsnreddy]

Thnx sir u cleared my confusion on am and GM

[humblestudent]

For non coaching students, these videos are very helpful sir ... 🙏
Please make more videos as all students can't go to Kota 😢😢

[ramyasriyaboyapally]

Are we always supposed to do am greater than or equal to gm .Or gm greater than or equal to hm also, in finding range sir

[roopnarayanchourasiya]

u r the best ...
wish u to be the biggest hit on youtube...😘

[nirajsoldier]

Thanku so much sir 🙏🙏🙏🙏
I was suffering from 2 days fromAM
and GM problem in trigo

[ishaangautam]

Very nicely 👌 explained short, crisp and to the point thank you very much

[rahuldubey]

Thanks DJ Sir u teaching style is very fantastic.👌😊

[darkdays]

Wow Sir, that's really fantastic.... Thank you Sir... This helped a lot to clear my confusion

[AmanGupta-fejk]

Thankyou sir for such a class of teaching( i love the way)

[dimitribharae]

For the HW problem..Im getting Sin^4(x) = b^2/a^2 is it not valid for all cases..Only for [0, 1]..

[sarabjotsingh]

Sir plz upload reaction mechanism of organic chemistry

[NeevTHM]

Applications of the inequality:
1. Finding the range of algebraic functions
2. Product-sum questions
3. Finding the range of trigonometric expressions

AM=GM when the numbers are equal (d=0, r=1)
Quantities have to be positive
Check for equality by equating the quantities
Split terms into equal parts when needed such the number of equal parts is the same as the power that the original term was raised to

[anushrevankar]

superb video, amazing explanation SIR

[thecrew]

Thank you so much sir
Well understood!