There is a more simple way to solve that... Since m2-m3 is bigger thant 0, m should be smaller than one and positive, there fore, you can rewrite the m as a/b. Then, (a/b)^2-(a/b)^3=3/64; a^2/b^2-a^3/b^3=3/64; (b*a^2-a^3)/b^3=3/64. Here you can igualate numerator to numerator, denominator to denominator, and then you obtain b*a^2-a^3=3 and b^3=64. Here you can obtain b=4; The numerator equation is 4a^2-a^3=3; which can be resolved using Ruffini
Life is simple, math is not... It can take me months if hard studying to understand but even if I can't get there, I'm willing to spend time just to keep listening to the music... So spanish. Regards from TIJUANA, Baja California, México. ❤
Multiply both sides by 64, let u=4m. u^3-4u+3=0 has a clear solution of 1, or m=1/4. This leaves u^2-3u-3=0. Then u=(3+/-sqrt(21))/2, for m=(3+/-sqrt(21))/8.
Imo a fraction is an uncalculated division, so I would write the result as .25 To me it seems like having an equation (division/fraction) as a result is not finalizing the problem. Resolving the fraction into its decimal representation is the ultimate final answer. I wonder if others feel this way. Thumbs up if you are in agreement with me folks and down if you don't.
I prefer solving quadratic to cubic equations. A value of 3/64 on the RHS. The presence of a cubic on the LHS led me to investigate the cube root of 64, 4. Investigating 1/4 gives 3/64 from (1/4)^2 - (1/4)^2 on the LHS. Sufficient to reduce the problem to a quadratic. My background involved a great deal of back fitting equations to material properties and using other people's backfits. Throughout judgement of any results, and backfit methodology was essential : recognizing the dominant source/sources of error drove the methodology.
m² - m³ = m²(1 - m) = 3/64. My first guess is that m is of the form 1/2ⁿ. More specifically, if 1 - m = 3/4 , then m would be 1/4 and this works! m = 1/4 is a solution, so dividing (m - 1/4) into m² - m³ - 3/64 = 0 and we find the quadratic factors and we can solve that with the quadratic formula.
Well...I got the first solution by inspection m = 1/4 Then I used (m-a)(m-b)(m-1/4) = 0 to get a cubic. Turn the resulting equation negative to get a coefficient of -1 for the m³ term. Next, set the coefficient of the m² term to be 1 and set the constant term equal to -3/64. You then solve two equations for the unknown "a" and "b", getting the final two solutions of m = (3±sqrt(21))/8
Muchas gracias Math Master por mostrar el paso a paso y los tricks matemáticos que demuestran la habilidad matemática que se debe tener para simplificar los cálculos y llegar a los 3 valores que satifacen la ecuación cúbica. Las demas persona que muestran otros trucos para simplificar la ecuacion desde el incio tambien demuestran tener habilidad matematica que se logra practicando y analizando ecuaciones en el papel no usando Mathlab. Gracias a todos los entusiastas de las matemáticas por mostrar sus conocimientos y compartirlos para todos. Estuvo genial la musica Andina de Fondo.
Thanks a lot Math Master for showing the step by step and mathematical tricks that demonstrate the mathematical ability that must be had to simplify the calculations and arrive at the 3 values that satisfy the cubic equation. The other people who show other tricks to simplify the equation from the beginning also demonstrate mathematical ability that is achieved by practicing and analyzing equations on paper not using Mathlab. Thanks to all the math enthusiasts for showing your knowledge and sharing it for everyone. The Andean Music in the background was also perfect.
By these video, you get a perfect example what happens, when an unprofessional amateur starts to "teach" mathematics... Calling himself "math master" and his standard school polynomial equation as an "olympiad" task...
- m^3 + m^2 = 3/64
Utilicemos el método de derivadas Parciales.
F(x)-m^3 = - 3m^2
- 3m^2 + m^2 = - m^2
-m^2 = 3/64
F'(x)- m^2 = - 2m
- 2m = 3/64
m =3/64 / - 2
m = - 0.02343
One value is m =1/4, two more can be found by solving rest of the quadratic equation.
There is a more simple way to solve that...
Since m2-m3 is bigger thant 0, m should be smaller than one and positive, there fore, you can rewrite the m as a/b.
Then, (a/b)^2-(a/b)^3=3/64;
a^2/b^2-a^3/b^3=3/64;
(b*a^2-a^3)/b^3=3/64.
Here you can igualate numerator to numerator, denominator to denominator, and then you obtain b*a^2-a^3=3 and b^3=64. Here you can obtain b=4; The numerator equation is 4a^2-a^3=3; which can be resolved using Ruffini
Life is simple, math is not... It can take me months if hard studying to understand but even if I can't get there, I'm willing to spend time just to keep listening to the music... So spanish.
Regards from TIJUANA, Baja California, México. ❤
Multiply both sides by 64, let u=4m.
u^3-4u+3=0 has a clear solution of 1, or m=1/4. This leaves u^2-3u-3=0.
Then u=(3+/-sqrt(21))/2, for m=(3+/-sqrt(21))/8.
Excellent!!!! Cubic ecuation = 3 answers.
Imo a fraction is an uncalculated division, so I would write the result as .25
To me it seems like having an equation (division/fraction) as a result is not finalizing the problem.
Resolving the fraction into its decimal representation is the ultimate final answer.
I wonder if others feel this way.
Thumbs up if you are in agreement with me folks and down if you don't.
I prefer solving quadratic to cubic equations.
A value of 3/64 on the RHS. The presence of a cubic on the LHS led me to investigate the cube root of 64, 4. Investigating 1/4 gives 3/64 from (1/4)^2 - (1/4)^2 on the LHS. Sufficient to reduce the problem to a quadratic.
My background involved a great deal of back fitting equations to material properties and using other people's backfits. Throughout judgement of any results, and backfit methodology was essential : recognizing the dominant source/sources of error drove the methodology.
64m²-64m³=3 ou encore
4(4m)²-(4m)³=3.
On pose M=4m alors 4M²-M³=3.
M³-4M²+3=0.
1 est une solution évidente.
La division par M-1 est plus simple.
m² - m³ = m²(1 - m) = 3/64.
My first guess is that m is of the form 1/2ⁿ.
More specifically, if 1 - m = 3/4 , then m would be 1/4 and this works!
m = 1/4 is a solution, so dividing (m - 1/4) into m² - m³ - 3/64 = 0 and we find the quadratic factors and we can solve that with the quadratic formula.
Well...I got the first solution by inspection
m = 1/4
Then I used (m-a)(m-b)(m-1/4) = 0 to get a cubic.
Turn the resulting equation negative to get a coefficient of -1 for the m³ term.
Next, set the coefficient of the m² term to be 1 and set the constant term equal to -3/64.
You then solve two equations for the unknown "a" and "b", getting the final two solutions of m = (3±sqrt(21))/8
Muchas gracias Math Master por mostrar el paso a paso y los tricks matemáticos que demuestran la habilidad matemática que se debe tener para simplificar los cálculos y llegar a los 3 valores que satifacen la ecuación cúbica. Las demas persona que muestran otros trucos para simplificar la ecuacion desde el incio tambien demuestran tener habilidad matematica que se logra practicando y analizando ecuaciones en el papel no usando Mathlab. Gracias a todos los entusiastas de las matemáticas por mostrar sus conocimientos y compartirlos para todos. Estuvo genial la musica Andina de Fondo.
1/4, by inspection.
m3 is complex number.
I can solve it ❤❤❤❤❤
m2-m2= 0
ارسمي خط الكسر قبل كتابة العناصر الرقمية .
Okk in next.
Thanks a lot Math Master for showing the step by step and mathematical tricks that demonstrate the mathematical ability that must be had to simplify the calculations and arrive at the 3 values that satisfy the cubic equation. The other people who show other tricks to simplify the equation from the beginning also demonstrate mathematical ability that is achieved by practicing and analyzing equations on paper not using Mathlab. Thanks to all the math enthusiasts for showing your knowledge and sharing it for everyone. The Andean Music in the background was also perfect.
Thank you so much for your kind words.
ممتاز GOOD
m= 1/4
m^2--(m^3/2)^2=4/64--1/64=(1/4)^2--(1/8)^2
By these video, you get a perfect example what happens, when an unprofessional amateur starts to "teach" mathematics... Calling himself "math master" and his standard school polynomial equation as an "olympiad" task...
Any problem related to qus???
Энг кийин йол экан соддарок варианти бору
5:52How was m+1/4 omitted?
LCM of 1/4 and 1/16 also m/2 and m.
Ez nem megoldás. Ez nem más, mint a megsejtés igazolása.
Szornyű, hogy ez a tudálékos okoskodás kering.
4/64-1/64.
m^2+m^3=5,625. m=?
I'm lost sir , I won't attend the class for today
Check previous vedios.
Didática zero.... Nem dá para acompanhar....
괄호도 제대로 못 맞추는 수준이라니...
Nei vari passaggi ti sei perso una parentesi 😅
m3 no puede ser solución. m3 es negativo y las soluciones tienen que estar en el intervalo (0,1)
Bravo
0.25 or circa -0.1978
or 0.9478