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Oksi-84 [34.3K]
2 years ago
14

Dentro de 11 años, la edad de Federico será la mitad del cuadrado de la que tenía hace 13 años. Calcula la edad de Federico.

Mathematics
1 answer:
Bad White [126]2 years ago
7 0

Plantearemos una ecuación cuadratica, y resolviendola veremos que Federico tiene 21 años.

<h3>¿Como plantear la ecuación que debemos resolver?</h3>

Lo primero que debemos hacer es definir la variable que vamos a usar, en este caso usare:

F = edad de Federico.

Dentro de 11 años, la edad de Federico será:

F + 11

Hace 13 años, la edad de Federico era:

F - 13

Reemplazando eso en lo que el problema plantea, tenemos:

(F + 11) = 0.5*(F - 13)^2

Ahora podemos resolver esto para F.

F + 11  = 0.5*(F^2 - 26*F +169)

F + 11 = 0.5*F^2 - 13*F + 84.5

Movemos todo al mismo lado:

F + 11 - 0.5*F^2 + 13*F - 84.5 = 0

-0.5*F^2 + 14*F - 73.5 = 0

Ahora tenemos una ecuación cuadratica, la cual resolvemos usando la formula de Bhaskara:

F = \frac{-14 \pm \sqrt{(14)^2 - 4*(-0.5)*(-73.5)} }{2*(-0.5)}  =\frac{-14 \pm 7}{-1}

Esto nos da dos valores:

  • F = (-14 + 7)/-1 = 7
  • F = (-14 - 7)/-1 = 21

El problema con el primer valor, es que es inconsistente con el enunciado, ya que en ese caso, Federico hace 13 años tendría una edad negativa. Así que <u>descartamos la primer solución</u> y nos quedamos con la segunda.

F = 21

Federico tiene 21 años.

Sí quieres aprender más sobre ecuaciones cuadraticas, puedes leer:

brainly.com/question/17102578

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