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

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  • Опубліковано 1 лют 2025

КОМЕНТАРІ • 44

  • @rishudubey1533
    @rishudubey1533 Рік тому +5

    Your vdos make my mood fresh
    Thankyou ❤️dear ❤️

    • @PreMath
      @PreMath  Рік тому +1

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

  • @prbmax
    @prbmax Рік тому +7

    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
      @PreMath  Рік тому +2

      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
      @alexwhite7756 Рік тому

      Many thanks for this summary. 😊

  • @devondevon4366
    @devondevon4366 Рік тому +1

    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
    @weggquiz Рік тому

    very well explained

  • @HappyFamilyOnline
    @HappyFamilyOnline Рік тому

    Very well explained👍
    Thanks for sharing😊

  • @KAvi_YA666
    @KAvi_YA666 Рік тому

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

    • @PreMath
      @PreMath  Рік тому +1

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

  • @Vedant-Goyal
    @Vedant-Goyal Рік тому +3

    👍👍 please make videos on trigonometry

    • @PreMath
      @PreMath  Рік тому +2

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

  • @davidfromstow
    @davidfromstow Рік тому

    Thank you, as always

  • @sahiljain1679
    @sahiljain1679 Рік тому

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

    • @Abby-hi4sf
      @Abby-hi4sf Рік тому +1

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

  • @dietrichschoen7340
    @dietrichschoen7340 Рік тому

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

  • @dandeleanu3648
    @dandeleanu3648 Рік тому

    why don't you use synthetic division?

  • @bentels5340
    @bentels5340 Рік тому +1

    Solved it essentially the same way.

    • @PreMath
      @PreMath  Рік тому

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

  • @saurabhkumar-in3om
    @saurabhkumar-in3om Рік тому +2

    Please series on number system

    • @PreMath
      @PreMath  Рік тому +2

      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
      @pritamyadav17 Рік тому +2

      Sir,are your nationality is American??

    • @PreMath
      @PreMath  Рік тому

      @@pritamyadav17 Yes!

  • @КатяРыбакова-ш2д

    Замена: X^7=m, X=3^(1/7).

  • @alster724
    @alster724 Рік тому +1

    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
    @guidosillaste4297 Рік тому

    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
      @vanshajshukla6205 Рік тому

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

    • @guidosillaste4297
      @guidosillaste4297 Рік тому

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

  • @NITINCHAUHA62
    @NITINCHAUHA62 Рік тому +3

    I solved it without any problem

    • @PreMath
      @PreMath  Рік тому +2

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

    • @pritamyadav17
      @pritamyadav17 Рік тому +2

      Could you share your solution@Nitin

    • @NITINCHAUHA62
      @NITINCHAUHA62 Рік тому +1

      @@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
    @giuseppemalaguti435 Рік тому

    x=sqrt7(3)

  • @naveenfulwariya5286
    @naveenfulwariya5286 Рік тому

    X = 3^1/7

  • @bigm383
    @bigm383 Рік тому +1

    🥂👍❤

    • @PreMath
      @PreMath  Рік тому

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

  • @NANICU
    @NANICU Рік тому

    ChatGPT couldn't solve this equation.

  • @vivekscreation8668
    @vivekscreation8668 Рік тому +1

    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!

  • @chrisc3895
    @chrisc3895 Рік тому

    :DDDDD