
English: 
[No Text]
There is a very interesting different way of solving a ...
quadratic equation: by iteration!
For example, the solutions of the quadratic ...
equation x^2−x−10=0, can be approximated.
By using the equation x=1+10/x
This has solutions given by the infinite continued iteration
We can easily show that the sequence of numbers gives ...
better and better approximations to one of the ...
solutions of the quadratic equation.
How many iterations do you estimate we'll need until the ...
approximation is good enough?
Stop the video here and take a guess!
The solutions of the quadratic can be visualised as the ...

Spanish: 
 
Podemos resolver ecuaciones cuadraticas
de forma diferente: usando repeticiones!
Por ejemplo, las soluciones de la ecuacion
se pueden aproximar usando la ecuacion
resultante de despejar x.
Esta ecuacion nos va a ayudar
a aproximar para una de las soluciones.
Cuanto mas repitamos el proceso,
mas se acercara al valor exacto de la solucion.
Cuantas veces crees que tenemos que repetirlo?
Para el video y piensa la respuesta!
La solucion a la ecuacion cuadratica

English: 
x-intercepts of the parabola which coincide with the ...
intersections of the graphs y=x and y=1+10/x.
When we use the iteration formula starting with 1,
the value of x gets closer and closer to the positive solution ...
of our quadratic equation. But, why?
The vertical line through x=1 stops at the y-value 1+10/1.
Stops at 11!Drawing a horizontal line we can use this ...
y-value as our next x-value and repeat the iteration.
The second vertical line through x=11 stops at the ...
y-value 1+10/11. Stops at 1.9!Drawing a ...
horizontal line we can use this coordinate as our next x-value and repeat.
The third vertical line through x=1.9 stops at the y-value 6.2 ...
that we use in our next iteration as a starting point by ...
drawing a horizontal line

Spanish: 
son los puntos donde la parabola cruza el eje de las x.
Esto equivale a los puntos donde
y=x intersecciona con y=1+10/x.
Cuando calculamos 1+10/x empezando por 1,
el valor se aproxima mas y mas, pero...por que?
Si sustituimos 1 en la ecuacion, resulta 11.
Este valor lo usaremos de nuevo.
De ahi que dibujemos otra linea vertical.
Esta para en 1.9!
Dibujando la linea horizontal, podemos reusar 1.9.
La tercera repeticion,
empezando en 1.9, resulta en 6.2.

English: 
The fourth vertical line through x=6.2 stops at the y-value 2.6.
The fifth is 4.8, the sixth is 3.0…
The seventh is 4.2
We need to repeat the iteration 13 times to reach 3.7.
It is easy if you type 1+10/ANS in your calculator ...
for each iteration.
The question for you to think about is:
will this method work with the other solution of our quadratic ...
equation? If you think the answer is yes,
share with us the starting point.
If you think the answer is no, tell us why.
[No Text]

Spanish: 
La cuarta repeticion, resulta en 2.6
La quinta en 4.8, la sexta en 3.0,
la septima en 4.2...
Necesitmos 13 repeticiones para aproximarnos a 3.7.
Es muy facil usar la calculadora...
...y repetir 1+10/ANS.
La pregunta es: funcionara con la otra solucion?
Si piensas que si, dinos el valor inicial de x.
Si piensas que no, explica tus razones.
No te olvides de suscribirte y darle al me gusta!
 
