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Ecuaciones cuadráticas
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Múltiples ejercicios y problemas (con sus respuestas) resueltos con los 3 diferentes tipos de métodos (factorización, completar el trinomio cuadrado perfecto y fórmula general).
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Actividad semana generadora C4I.- Una vez que ya aprendimos los tres métodos para resolver ecuaciones
cuadráticas es importante ponerlos en uso, ¿cómo? resolviendo problemas
A continuación encontrarás 12 problemas, resuelve 4 con el método de
fórmula general, 4 con factorización y 4 con completando el trinomio
cuadrado perfecto.
1.- La suma de dos números es 5 y su producto es −84. Halla dichos números.
x+y=5 x=5-y
(x) (y) = -84
(5 - y) (y) = -84
5y - y2 = -84
5y - y2 + 84 = 0
Trinomio cuadrado imperfecto caso 1
y2 - 5y -84 = 0
(y - 12 ) (y + 7 )
y-12 = 0 y= 12
y + 7= 0 y= -7
R: Los números son -7 y 12
a= -1 b = 5 c = 84
x1,2 = -5 +- 5² − 4( − 1)(84/ 2 ( -1)
x1,2 = -5 +- 25 + 336/ -2
x1,2 = - 5 +- 361 / -2
x1,2 = -5 +- 19 / -2
x1= -5 + 19 / -2 = -7
x2 = -5 -19 / -2 = 12
, 2.- Dentro de 11 años la edad de Pedro será la mitad del cuadrado de la edad
que tenía hace 13 años. Calcula la edad de Pedro.
(x + 11) = (x -13)2 /2
(x + 11) (2) = (x - 13)2
2x + 22 = x2 - 26x + 169
x2 -26x - 2x + 169 - 22 = 0
x2 -28x + 147 = 0
( x - 7 ) ( x - 21 )
x-7=0
x=7
x - 21 = 0
x = 21
x = - (-28) + − 282 - 4 (1) (147) / 2 (1)
x = 28 + 784 -
x = 28 +
x = 28 + 14 /2
x1 = 28 +
x1 = 21
x2 = 28 -
x2 = 7
La edad de pedro es 21
3.- Para cercar una finca rectangular de 750 m² se han utilizado 110 m de cerca.
Calcula las dimensiones de la finca.
(x) (y) = 750
2x + 2y = 110
x = 110 - 2y / 2
x = 55 - y
(55 - y) (y) = 750
55y - y2 = 750
55y - y2 - 750 = 0
y2 - 55y + 750 = 0
(y - 25 ) (y - 30 )
y - 25= 0 y = 25
y - 30 = 0 y = 30
Las dimensiones son 25m y 30m
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