Germany l can you solve?? l Hardest Olympiad Math problem

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[@pietergeerkens6324]

Simon's Favourite Factoring Trick: Multiply the flattened equation through by 8/8 to get
x³ = ⅛ ⋅ ( 40⋅√37 - 112 )
= ⅛ ⋅ ( 37⋅√37 + 3 √37 - 111 - 1 )
= ½³ ⋅ ( (√37)³ - 3⋅(√37)² + 3⋅√37 - 1³ )
= ½ ⋅ (√37 - 1).
No spurious root appears, and the other two roots are complex.
Fancy tricks are fine when they're actually needed - but simple tricks are always better when applicable.

[@pablocopello3592]

The statement of the problem should say: "express the solution (x) without using cubic rooth", otherwise I do not see why the straight fordward x=cbrt(5*sqrt(37)-14) is not a valid solution.
The method used do not contribute anything, it does not solve general problems, only works and is used because the numbers in the problem were "engineered". If this kind of crappy methods are valid, so I have a better method: substitute x by (sqrt(37)-1)/2 and you will see that this is the solution (only (real) solution, because x^3 is a strictly monotonous increasing function).

[@SeekingTheLoveThatGodMeans7648]

From the cbrt, one can substitute x with y + z sqrt(37) and cube both sides and solve the rational and irrational parts as a system, right?

[@Марія-75]

Спасибо за работу и ученье

[@ArkadiyOur]

У меня получилось 3

[@roselanggin958]

I can usually follow these but I lost it the line after 'xing 1 and 2.'

[@ApsisApocynthion]

Yeah it’s confusing and instead of explaining it, we have this terrible music on loop. So not only do we not learn anything, we have to mute the video.

[@andresrebolledobanquet1924]

X^3 + 14 = 5 *5.56776
x^3 + 14 = 27.83882
x^3 = 27.83882 - 14
x^3 = 13.83882
F(x)x^3 = 3x^2
F'(x)3x^2 = 6x
6x = 13.83882
x = 13.83882/6
x = 2.30647
2.30647*3*2 + 14/ 5.56776 = 5
27.83882 / 5.56776 = 5
5 = 5

[@anthonysaverio5003]

X=2.541

[@webanut]

sqrt18,5 - 0,5.

[@риколай-щ3ю]

почему х больше нуля просто сделать проверку

[@JorgeluisHerrera-g9l]

Sí la matemática es fascinante, pero por favor cambien de canción.

[@риколай-щ3ю]

почему х больше нуля, ведь корнь нечетной степени

[@hassanlamghairbat]

h

[@user-qr7dw4hk6x]

На третьей строчке вернулись к первой.что это за дурь?

[@ВалентинаБулановская]

Ге понтмаю зач5м дишнее действие во всех примерах.
кто вас усит так делать?
ах =5 тогда х= 5/а
зачем делить обе стороны на а?😂😂😂😂😂
ах/а=5/а лишнее это

[@АрпикАгавелян]

Не рациональный ход решения

[@vladiksavochkin6769]

Если есть условие x>0 то решений нет

[@Kidus.Lalibela]

Moran germy dog

[@josefsezbrisko9064]

x = 2,541(38127)