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Clase 14

Clase 14. Ejercicios sobre ecuaciones con radicales. x – 1. x + 1. √. x – 1 + x – 4. = x – 5. =. √. √. x – 1. x + 2. Para el estudio individual. Determina el conjunto solución de las siguientes ecuaciones:. a). S = { 7 }. b). S = { 5 }. (x – 4 ) √ x – 1.

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Clase 14

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  1. Clase 14 Ejercicios sobre ecuaciones con radicales

  2. x – 1 x + 1 √ x – 1 + x – 4 = x – 5 = √ √ x – 1 x +2 Para el estudio individual Determina el conjunto solución de las siguientes ecuaciones: a) S = {7 } b) S = {5 }

  3. (x – 4) √ x – 1 √ x – 1 ● x + 1 √ x – 1 + x – 4 = √ x – 1 = x – 1 + (x – 4) √ x – 1 2 2 2 = (x – 4)2 (x – 1 ) 4 = 4 = (x2 – 8x + 16)(x – 1) 4 = x3–8x2 +16x –x2 +8x –16 0 = x3–9x2 +24x –20

  4. x3–9x2 +24x –20 = 0 = 0 x – 5 = 0 ó x – 2 = 0 x2 = 2 x1 = 5 1 – 9 24 –20 –20 20 5 5 0 – 4 4 1 (x – 5)(x – 2)2

  5. Ejercicio Resuelve las siguientes ecuaciones: a) √ x + 5 + 1 = x b) x –√9 + x √x2 – 3 = 3

  6. a) √ x + 5 + 1 = x 2 √ x + 5 = x – 1 ( )2 x + 5 = x2 – 2x + 1 x2 – 3x – 4=0 (x – 4)(x + 1) = 0 x – 4= 0ó x + 1= 0 x1= 4 x2= – 1

  7. = √9 +1 = √4 +1 MI:√4 + 5 + 1 MI:√–1 + 5 + 1 Comprobación para x1= 4 = 3+1 = 4 MD:4 comparación:4 = 4 para x2= –1 = 2+1 = 3 MD:–1 comparación:3 ≠ –1

  8. = 9 + x√x2 – 3 = x√x2 – 3 b) x –√9 + x√x2 – 3 = 3 2 x – 3 = √9 + x√x2 – 3 ( )2 x2 – 6x + 9 2 ( )2 x2 – 6x x4–12x3+36x2 = x2(x2 – 3) x4–12x3+36x2 = x4– 3x2 12x3 – 39x2 = 0

  9. 13 x2 = 4 12x3 – 39x2 = 0 3x2 (4x – 13) = 0 x1 = 0 ó 4x – 13 = 0

  10. √2 – x = 1 – √x – 1 15 A(x) + = 8 A(x) Para el estudio individual 1. Determina el conjunto solución de la siguiente ecuación: Resp. S = 1  3 2.Sea A(x) = √x2 + 9 . Determina para que valores de x se cumple: Respuestax = 4 ; 0

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