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.
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).
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.
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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.
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).
Спасибо за работу и ученье
I can usually follow these but I lost it the line after 'xing 1 and 2.'
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.
sqrt18,5 - 0,5.
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
X=2.541
почему х больше нуля, ведь корнь нечетной степени
Sí la matemática es fascinante, pero por favor cambien de canción.
h
На третьей строчке вернулись к первой.что это за дурь?
Не рациональный ход решения
x = 2,541(38127)
Moran germy dog