Mathematical Olympiad | Solve and Check the Radical Rational equation | Math Olympiad Training

แชร์
ฝัง
  • เผยแพร่เมื่อ 8 ก.พ. 2025
  • Learn how to Solve and Check the Radical Rational equation. Step-by-step tutorial by PreMath.com
    Today I will teach you tips and tricks to solve the given olympiad math question in a simple and easy way. Learn how to prepare for Math Olympiad fast!
    Step-by-step tutorial by PreMath.com
    • Mathematical Olympiad ...
    Need help with solving this Math Olympiad Question? You're in the right place!
    I have over 20 years of experience teaching Mathematics at American schools, colleges, and universities. Learn more about me at
    / premath
    Mathematical Olympiad | Solve and Check the Radical Rational equation | Math Olympiad Training
    #OlympiadMathematics #OlympiadPreparation #CollegeEntranceExam
    #PreMath #PreMath.com #MathOlympics #HowToThinkOutsideTheBox #ThinkOutsideTheBox #HowToThinkOutsideTheBox?
    #OlympiadMathematicalQuestion #HowToSolveOlympiadQuestion #MathOlympiadQuestion #MathOlympiadQuestions #OlympiadQuestion #Olympiad #AlgebraReview #Algebra #Mathematics #Math #Maths
    #MathOlympiadPreparation #LearntipstosolveOlympiadMathQuestionfast #OlympiadMathematicsCompetition #MathOlympics #SolveSystemofEquations
    #blackpenredpen #LearnHowToSolveOlympiadQuestionQuickly #LinearEquations #RadicalEquations #ExponentialEquation #ExponentialEquations #RadicalEquation
    #PoShenLoh #OlympiadMathematics
    #SolveandChecktheRadicalRationalEquation #SolveandCheck #RadicalRationalEquation
    #MathOlympiadTraining
    How to solve Olympiad Mathematical Question
    How to prepare for Math Olympiad
    How to Solve Olympiad Question
    How to Solve international math olympiad questions
    international math olympiad questions and solutions
    international math olympiad questions and answers
    olympiad mathematics competition
    blackpenredpen
    Po-Shen Loh
    Po Shen Loh
    math olympics
    olympiad exam
    olympiad exam sample papers
    math olympiad sample questions
    math olympiada
    British Math Olympiad
    olympics math
    olympics mathematics
    olympics math activities
    olympics math competition
    Math Olympiad Training
    How to win the International Math Olympiad | Po-Shen Loh and Lex Fridman
    Po-Shen Loh and Lex Fridman
    Number Theory
    There is a ridiculously easy way to solve this Olympiad qualifier problem
    This U.S. Olympiad Coach Has a Unique Approach to Math
    The Map of Mathematics
    mathcounts
    math at work
    exponential equation
    system of equations
    solve system of equations
    solve the equation
    Linear Equation
    Radical Equation
    Learn how to solve Olympiad Question quickly
    pre math
    Olympiad Mathematics
    Rational equation
    Math Olympiad Training
    Solve and Check the Radical Rational equation
    Radical Rational equation
    How to check answers
    Subscribe Now as the ultimate shots of Math doses are on their way to fill your minds with the knowledge and wisdom once again.

ความคิดเห็น • 77

  • @FaixaPretanoENEM
    @FaixaPretanoENEM 2 ปีที่แล้ว +7

    Calm and perfect step by step resolution, as usual. Thanks, professor!

    • @PreMath
      @PreMath  2 ปีที่แล้ว +3

      You are very welcome.
      So nice of you.
      Thank you for your feedback! Cheers!
      You are awesome, CRMF 😀

  • @fevengr9245
    @fevengr9245 2 ปีที่แล้ว +3

    Consistent with my talent for finding the more difficult approach:
    I set P=(x-6)/(x+10) and 1/P = (x+10)/(x-6). It took more time but I did finally get the correct answer. That was a clever problem!

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      Thank you for your nice feedback! Cheers!
      You are awesome. Keep it up 😀

    • @jbreezy101
      @jbreezy101 2 ปีที่แล้ว +1

      Lol. But you got there

  • @242bluewater9
    @242bluewater9 2 ปีที่แล้ว +3

    love this radical rational equation question, your step-by-step solution is awesome bro, 242 math here

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Glad to hear that!
      Thank you for your feedback! Cheers!
      You are awesome 😀

  • @dantallman5345
    @dantallman5345 2 ปีที่แล้ว

    Beautiful problem. It got under my skin and I spent way more time on it than I will ever admit. It’s remedial math time for a retiree.
    btw- The starting equations are a circle centered at 0,0 with radius sqrt(7) and and a cubic that looks roughly like a bell curve riding on a baseline y=-x. The two solutions are at the intersections of circle and bell.

  • @waheisel
    @waheisel 2 ปีที่แล้ว +3

    Another way to solve is to let u=x+2 which gives sqrt((u-8)/(u+8)) etc. You end up with u=+or-17. I always look forward to the daily PreMath puzzle. Thanks!

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      You are very welcome.
      Keep watching
      Thank you for your feedback! Cheers!
      You are awesome, William 😀
      Love and prayers from, Arizona, USA!

    • @actions-speak
      @actions-speak 2 ปีที่แล้ว +1

      I did the same substitution and the cancellation was very satisfying!

  • @anatoliy3323
    @anatoliy3323 2 ปีที่แล้ว +3

    Nice a task as always! I have solved it in the same way. Thank you, Professor! My congratulations on the Easter Holiday

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      May this Easter bring PEACE to Ukraine!
      Thank you for your feedback! Cheers!
      You are awesome, Anatoliy. Stay safe and blessed 😀
      Love and prayers from the USA!

  • @ignacy7474
    @ignacy7474 2 ปีที่แล้ว

    Actually, youre my favourite channel on TH-cam

  • @careerpk2904
    @careerpk2904 2 ปีที่แล้ว

    Your way of method is amazing

  • @ManjulaMathew-wb3zn
    @ManjulaMathew-wb3zn ปีที่แล้ว

    I like your method as always. Alternatively you could simply square both sides which will remove all radicals in one shot leaving a quadratic equation in terms of x right away. The two radiants being reciprocal s made the usually nasty middle term simply equal to two and made the rest of the numbers relatively smaller.
    Cheers!

  • @predator1702
    @predator1702 2 ปีที่แล้ว +1

    Very nice solution👍. Thank you teacher 🙏.

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      You are very welcome.
      Glad to hear that!
      Thank you for your feedback! Cheers!
      You are awesome 😀
      Love and prayers from the USA!

  • @KAvi_YA666
    @KAvi_YA666 2 ปีที่แล้ว +1

    Thanks for video. Good luck sir!!!!!!
    Nicely and super!!!!!!!!!

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      You are very welcome.
      Thank you for your feedback! Cheers!
      You are awesome 😀
      Love and prayers from the USA!

  • @pragnyaparamitadwibedy622
    @pragnyaparamitadwibedy622 2 ปีที่แล้ว +2

    Did this question with ease thank you sir

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      .
      Excellent!
      Glad to hear that!
      Thank you for your feedback! Cheers!
      You are awesome, Soumik 😀

  • @242math
    @242math 2 ปีที่แล้ว +1

    very well done, thanks for sharing the solution to this radical rational equation

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      You are very welcome.
      So nice of you.
      Thank you for your feedback! Cheers!
      You are awesome, my dear friend 😀

  • @fouadhammout651
    @fouadhammout651 2 ปีที่แล้ว

    Saraha ma3andich zhar la f tssahib la f zwaj walit tangoul tawahad maynawad tawahda Matahmal... '' '

  • @divein2427
    @divein2427 2 ปีที่แล้ว +1

    this was very well explained, thanks for sharing bro

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      You are very welcome.
      So nice of you.
      Thank you for your feedback! Cheers!
      You are awesome, 242 😀

  • @sanaaarish7707
    @sanaaarish7707 2 ปีที่แล้ว +1

    Great Video!

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Glad you enjoyed it
      Thank you for your feedback! Cheers!
      You are awesome, Sana dear 😀

  • @SuperYoonHo
    @SuperYoonHo 2 ปีที่แล้ว

    perfect solution

  • @mahalakshmiganapathy6455
    @mahalakshmiganapathy6455 2 ปีที่แล้ว

    👌very nice explanation

  • @fretan3950
    @fretan3950 2 ปีที่แล้ว +2

    Another solution method would be to first square the equation, so that you have (x-6)/(x+10)+(x+10)/(x-6)+2=1156/225. This can then be simplified to 256/(x^2+4x-60)=256/225 so that x^2+4x-60=225 must be true. And that quadratic equation has the solutions x=15 and x=-19.

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      Great
      Thank you for your feedback! Cheers!
      You are awesome, Fretan 😀

    • @prabhudasmandal6429
      @prabhudasmandal6429 2 ปีที่แล้ว

      Simple one. Thanks

    • @vaibhavkrupakar240
      @vaibhavkrupakar240 2 ปีที่แล้ว +1

      -19 won't make sense

  • @xyz9250
    @xyz9250 2 ปีที่แล้ว

    I did it by squaring both side of the original equation, and after simplification, arrived x^2 + 4x - 285 = 0, from there got the same final answers.

  • @marcelowanderleycorreia8876
    @marcelowanderleycorreia8876 ปีที่แล้ว

    Professor, it is allowed to use calculator in such olympiad? By the way, congratulations for the resolution!!

  • @nicogehren6566
    @nicogehren6566 2 ปีที่แล้ว +1

    very nice question

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      So nice of you, Nico.
      Thank you for your feedback! Cheers!
      You are awesome 😀

  • @experimentingalgorithm1546
    @experimentingalgorithm1546 2 ปีที่แล้ว +3

    Sir can you make a video on proof of why
    If ax^a = bx^b
    then a = b

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      Great question to ask! Pretty soon.
      Thank you for asking! Cheers!
      You are awesome 😀

  • @mathfreak5702
    @mathfreak5702 2 ปีที่แล้ว +2

    Yay! Got the same.

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Bravo
      Glad to hear that!
      Thank you for your feedback! Cheers!
      You are awesome, Saitama. Keep rocking 😀

  • @pranavamali05
    @pranavamali05 2 ปีที่แล้ว +2

    Thnku

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      You are very welcome.
      Thank you for your feedback! Cheers!
      You are awesome, Pranav 😀
      Love and prayers from the USA!

  • @j.r.1210
    @j.r.1210 2 ปีที่แล้ว +5

    This equation also can be solved pretty quickly without a substitution. Just work through the algebra directly, eliminating the radicals, to end up with a huge but fun quadratic equation: 256x^2 + 1024x - 72960 = 0. This reduces to x^2 + 4x - 285 = 0, which is easy to factor as (x + 19)(x - 15).

    • @PreMath
      @PreMath  2 ปีที่แล้ว +2

      Great
      Thank you for your feedback! Cheers!
      You are awesome, JR 😀

    • @susennath6035
      @susennath6035 2 ปีที่แล้ว

      Thanks for ur reply.
      I definitely inform you as per your later example

  • @jim2376
    @jim2376 ปีที่แล้ว

    We want numerators and denominators that result in integer square roots. x = 15 works nicely since 15 + 10 = 25 and 15 - 6 = 9. That will give us (3/5) + (5/3). (9 + 25)/(5 x 3) = 34/15.

  • @tuandanganh7603
    @tuandanganh7603 2 ปีที่แล้ว

    Before solving, you need to set conditions for the variable, then there is no need to retest the solution of the equation

  • @SuperYoonHo
    @SuperYoonHo 2 ปีที่แล้ว

    thanks

  • @buff9943
    @buff9943 2 ปีที่แล้ว

    Спасибо за видео

  • @umeshmyumi3519
    @umeshmyumi3519 2 ปีที่แล้ว +1

    Nice 👍👍

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      So nice of you.
      Thank you for your feedback! Cheers!
      You are awesome, Umesh 😀
      Love and prayers from the USA!

  • @nirupamasingh2948
    @nirupamasingh2948 2 ปีที่แล้ว +1

    V nice

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      So nice of you.
      Thank you for your feedback! Cheers!
      You are awesome, Niru 😀

  • @kikiadewardani824
    @kikiadewardani824 2 ปีที่แล้ว

    jos temenan...

  • @ranveeryadav176
    @ranveeryadav176 2 ปีที่แล้ว

    15 by value putting method

  • @gouravsaini6928
    @gouravsaini6928 2 ปีที่แล้ว

    Please solve this problem- 5^x + 2^x = 5

  • @broytingaravsol
    @broytingaravsol 2 ปีที่แล้ว +1

    easy one

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Super
      Thank you for your feedback! Cheers!
      You are awesome 😀

  • @zplusacademy5718
    @zplusacademy5718 2 ปีที่แล้ว

    Very nice and beautiful ❤️

  • @sparshraj1367
    @sparshraj1367 2 ปีที่แล้ว +1

    I got it right ....😁

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Excellent!
      Thank you for your feedback! Cheers!
      You are awesome, Raj 😀

  • @Teamstudy4595
    @Teamstudy4595 2 ปีที่แล้ว +1

    Ans : x = 15. (*Easiest question )

  • @mathswan1607
    @mathswan1607 2 ปีที่แล้ว +1

    x=15 or x=-19

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Excellent!
      Thank you for your feedback! Cheers!
      You are awesome 😀

  • @olgakornak3969
    @olgakornak3969 2 ปีที่แล้ว

    9×25=225.

  • @open_mind5465
    @open_mind5465 2 ปีที่แล้ว

    😭
    I spent an hour trying and things scattered. In the end, I found that the solution is very simple
    😐

  • @susennath6035
    @susennath6035 2 ปีที่แล้ว

    Sometimes you r giving long sum rather than IQ based sum .
    I hope ,you will prefer IQ based sum more rather than this type of monotonous sum

    • @PreMath
      @PreMath  2 ปีที่แล้ว +1

      Dear Susen, please give an example to make this problem into an IQ based sum. Just want to see the glimpse!
      Thank you for your feedback! Cheers!

  • @olgakornak3969
    @olgakornak3969 2 ปีที่แล้ว

    34÷15=2.266666666666666666667.

  • @giuseppemalaguti435
    @giuseppemalaguti435 2 ปีที่แล้ว

    19,-15.....ho sbagliato e' -19,15

  • @victorfildshtein
    @victorfildshtein 2 ปีที่แล้ว

    In the Soviet school, we were taught that it is necessary to determine the range of acceptable values. Here:
    (x-6)/(x+10)⩾0 ⇒ [(x-6)⩾0 AND (x+10) ⩾0] OR [(x-6)⩽0 AND (x+10)⩽0] ⇒ x⩽-10 OR x⩾6