Solve and Check x^21 + x^14 = 36 for real solutions | Olympiad Mathematics | Math Olympiad Training

[@rishudubey1533]

Your vdos make my mood fresh Thankyou ❤️dear ❤️

[@PreMath]

Glad you think so! Thanks for your feedback! Cheers! You are awesome, Rishu. Keep it up 👍 Love and prayers from the USA! 😀

[@prbmax]

And now let's recall, Power Rule, Substitution, Solve Cubic Equation by grouping and factoring, Replace, Manipulation, Difference of two squares identity, Replace, Factor out, Distribute, Separate, Quadratic Formula, Discriminate Rule, Take root, Check solution, Basic Rule of roots, Power Rule. WOW!

[@PreMath]

You are correct, Paul. It's called scaffolding! Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@alexwhite7756]

Many thanks for this summary. 😊

[@devondevon4366]

Answer 1.17 or 3^1/7 let n=x^7 then n^3 + n^2 = 36 n = 3 as 3^3 + 3^2 = 36 hence 3 =x^7 3^1/7=x Answer 1.17= x Answer

[@matematicafacilcomprof.jua9231]

Very good! I found it easy, since I know that 36 is 3^3 + 3^2, it became easy to find out that x is 3^(1/7).

[@weggquiz]

very well explained

[@HappyFamilyOnline]

Very well explained👍 Thanks for sharing😊

[@davidfromstow]

Thank you, as always

[@Vedant-Goyal]

👍👍 please make videos on trigonometry

[@PreMath]

Already uploaded! More to come as well... Thanks for your feedback! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@KAvi_YA666]

Thanks for video.Good luck sir!!!!!!!!!!!

[@PreMath]

You are very welcome! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@sahiljain1679]

Excellent video, very well explained. I just want to ask how did you get: -3a^2 +4a^2 ?

[@Abby-hi4sf]

Grouping and fatoring means, we know 4 - 3 = 1 then you replace a^2 by -3a^2 +4a^2

[@dandeleanu3648]

why don't you use synthetic division?

[@saurabhkumar-in3om]

Please series on number system

[@PreMath]

Sure, more to come. I've already uploaded videos on this topic. Please check them out. Thanks for the suggestion. Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@pritamyadav17]

Sir,are your nationality is American??

[@PreMath]

@@pritamyadav17 Yes!

[@КатяРыбакова-ш2д]

Замена: X^7=m, X=3^(1/7).

[@bentels5340]

Solved it essentially the same way.

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@dietrichschoen7340]

x = e^(ln(3)/7)=1,1699

[@alster724]

I have an easier approach though... I used a combination of 3 methods 1.) Rational Zero Theorem 2.) Factor/Remainder Theorem 3.) Synthetic Division I listed down all the possible zeroes with the RZT (Rational Zero Theorem) and then with the Factor/Remainder Theorem, I substituted each value, but when I substituted a= 3 in the original equation, it resulted to 0. Thus a= 3 is the answer. To double check for other possible solutions, I proceeded with Synthetic Division and divided a³+a²-36 by a-3 Thus resulting in a²+4a+12 and followed the same procedure as stated in the video.

[@guidosillaste4297]

What is the solution if 7 root 3 is solved ? i really want to know the number. Will it be a endless o........ or will it have a end?

[@vanshajshukla6205]

Its a irrational number, so its non repeating and non terminating number , It will be endless like square root of 2 1.14115926535..........…..........................

[@guidosillaste4297]

@@vanshajshukla6205 So its endless muahaha . How to i use that value in real life then?

[@NITINCHAUHA62]

I solved it without any problem

[@PreMath]

Excellent! Thanks for sharing! Cheers! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@pritamyadav17]

Could you share your solution@Nitin

[@NITINCHAUHA62]

@@pritamyadav17 yes X^21 can be written as x^7×3 And x^14 can be written as x^7×2 Then here I suppose that x^7= y And then the equation x^21 + x^14=36 Can be written as y^3 + y^2= 36 Now solve this you got the answer which is {y=3} and x^7 = 3 Hence : x= 3^1/7

[@giuseppemalaguti435]

x=sqrt7(3)

[@naveenfulwariya5286]

X = 3^1/7

[@bigm383]

🥂👍❤

[@PreMath]

Super! Thanks for your continued love and support! You are awesome. Keep it up 👍 Love and prayers from the USA! 😀

[@vivekscreation8668]

If the points A(5,8), B(8,0), C(0,4), D(0,5) and O(0,0) are plotted on graph paper, then the point on x axis are a) A and C b) C and D c) only B d) B and O PLEASE HELP ME OUT!

[@Anonymous31416]

C) Only B

[@vivekscreation8668]

@@Anonymous31416 galat h

[@kitetm7596]

Just check if y=0 bro

[@vivekscreation8668]

@@kitetm7596 i know that but teel me the correct option bha

[@NANICU]

ChatGPT couldn't solve this equation.

[@chrisc3895]

:DDDDD