Japanese | Math Olympiad | How to solve for X in this problem ?

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  • @prabhudasmandal6429
    @prabhudasmandal64292 ай бұрын

    When we get x^2+71=0 or x^2=--71 ,we can easily say that it is not valid for real value .

  • @GaryBricaultLive
    @GaryBricaultLive2 ай бұрын

    By inspection I can see that the numerator and denominator are essentially symmetrical. And the obvious answer being X = 0.

  • @is7728

    @is7728

    2 ай бұрын

    Yes I noticed that too

  • @junkmail4613

    @junkmail4613

    2 ай бұрын

    I concur

  • @jim2376

    @jim2376

    2 ай бұрын

    Exactamundo.👍👍

  • @user-kz3tn5sr6t

    @user-kz3tn5sr6t

    Ай бұрын

    ​@@junkmail4613йффффффффффффффффффффффйф

  • @pb2806
    @pb28062 ай бұрын

    Interesting, so the key is to notice that 7+10=17 and 8+9=17, so that we can regroup the terms and obtain similar developments in the form of x^2+17x+constant. Thanks

  • @user-pd7js7cy9m
    @user-pd7js7cy9m2 ай бұрын

    If 0

  • @Nepomenik

    @Nepomenik

    2 ай бұрын

    Exactly! With added x>0 and not equal to 7, 8 ,9 or 10, this is the most elegant proof.

  • @scpforjee
    @scpforjeeАй бұрын

    5:51 Could have added 1 on both sides, then completed the square. So (a+1)²=(b+1)². Then take square root on both sides. So a+1=±(b+1) and then proceed.

  • @professorsargeanthikesclim9293

    @professorsargeanthikesclim9293

    Ай бұрын

    Excellent.

  • @antonellocossu4319
    @antonellocossu43192 ай бұрын

    By looking at the four factors composing the denominator, the solutions can't be 7, 8, 9 and 10. Furthermore, provided there are four factors at the denominator (an even number), and showing the same constants of the factors in the upper side of the fraction, with just their signs changed, it can be deduced that one solution in R is 0, like many comments correctly say below. From observing the equation there's another consequence: the shape of the resulting equation will be x^4+ax^3+bx^2+cx+d = x^4-ax^3+bx^2-cx+d where a, b, c, d >0 and the x terms power 0, 2, and 4 are the same on both sides of the equation. Hence, they will cancel each other, and the resulting equation will have the form ax^3+cx=0 where both a and c will be >0. Therefore, the resulting equation will have the form x(x^2+A)=0 (A=a/c) where A>0, which means that there's one only solution in R: x=0.

  • @benjaminconcepcion2102
    @benjaminconcepcion2102Ай бұрын

    By inspection x=0

  • @vladsmith3657
    @vladsmith36572 ай бұрын

    Easy, X=0. 👍

  • @habeebalbarghothy6320
    @habeebalbarghothy63202 ай бұрын

    Very clear ! x=0

  • @prime423
    @prime42314 күн бұрын

    Gary has it right!!Analyze first!!!!!!!

  • @keinKlarname
    @keinKlarname2 ай бұрын

    x^2 +71 = 0 discriminant to see there are no real solutions?

  • @samuelbenet007

    @samuelbenet007

    2 ай бұрын

    À cette équation, tu vois tout de suite que S={∅} ^^

  • @ToanPham-wr7xe
    @ToanPham-wr7xe2 ай бұрын

    😮

  • @MathSync
    @MathSyncАй бұрын

    I ❤ Mathematics

  • @learncommunolizer

    @learncommunolizer

    Ай бұрын

    Thank you very much!

  • @olegkalsin5020
    @olegkalsin50202 ай бұрын

    Доказать ответ, который лежит на поверхности...

  • @benjaminconcepcion2102
    @benjaminconcepcion2102Ай бұрын

    Solvable by the fastest way😭

  • @jim2376
    @jim23762 ай бұрын

    By inspection x = 0 works. (56 x 90)/(56 x 90) = 1. We're positive upstair and downstairs.

  • @user-jl9bs3ip5m
    @user-jl9bs3ip5mАй бұрын

    Уважаемые, скажите кому и для каких целей нужны такие уравнения? В школе так вообще замучаешься решать, один пример за урок, на большее времен не хватит.

  • @herbertklumpp2969
    @herbertklumpp29692 ай бұрын

    Nothi g to calculate.x=0 is a solution because 7*8*9*10= (-7)*(-8)*(-9)*(-10) For x real x+7 ,> x-7 and Rhein same for the other ( ) therefore nominator is greaterthan denominator conclude nominator/denom. Is 1 für Real x

  • @anjukhandu
    @anjukhandu2 ай бұрын

    I got answer in 1minute by putting value of x ....

  • @mauriziocotti9781
    @mauriziocotti97812 ай бұрын

    Very good

  • @learncommunolizer

    @learncommunolizer

    2 ай бұрын

    Thank you very much!!

  • @user-bk1wl9ez1c
    @user-bk1wl9ez1c2 ай бұрын

    Factorial

  • @user-ye6go4ft7q
    @user-ye6go4ft7q2 ай бұрын

    Зачем так длинно решать ??? (a+1)(a+2)/-{(a+1)}{-(a+2)}=1 при чёрном или -1 при печатном умножителей ???

  • @comdo777
    @comdo7772 ай бұрын

    asnwer=1x

  • @peterkrauliz5400
    @peterkrauliz5400Ай бұрын

    There is a second solution if we accept x to be infinitely large.

  • @ashrafmuhammad3187
    @ashrafmuhammad31872 ай бұрын

    X=0

  • @mariabetances3206
    @mariabetances3206Ай бұрын

    X=1

  • @user-ix5vk8re3h
    @user-ix5vk8re3h2 ай бұрын

    Х=0.

  • @ValentinTonev-bt4iz
    @ValentinTonev-bt4iz2 ай бұрын

    Х = 0

  • @anjukhandu
    @anjukhandu2 ай бұрын

    X=3 in one minute

  • @anjukhandu

    @anjukhandu

    2 ай бұрын

    For 1680 wala problem

  • @user-gy2xk3zc1c
    @user-gy2xk3zc1c2 ай бұрын

    Решение за 20 секунд. Х равен 0.

  • @user-ec5ip3vp2r
    @user-ec5ip3vp2r2 ай бұрын

    0

  • @NhaNguyen-cx1ri
    @NhaNguyen-cx1riАй бұрын

    X = + (‐) 1

  • @soheil1455
    @soheil1455Ай бұрын

    0

  • @favibezabh439
    @favibezabh439Ай бұрын

    X=0