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Ecuaciones con radicales

Clase 8. Ecuaciones con radicales. Algoritmo. 1. Aislar el radical. 2. Elevar ambos miembros al cuadrado. 3. Obtener la ecuación sin radical. 4. Resolver la ecuación. 5. Comprobar. a). x + 1 +. = 3. 3x + 4. – 5 = 0. 13 – 3x. b). +. 7x – 12. Ejercicio 1.

jordan-rogers
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Ecuaciones con radicales

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  1. Clase 8 Ecuaciones con radicales

  2. Algoritmo 1. Aislar el radical. 2. Elevar ambos miembros al cuadrado. 3. Obtener la ecuación sin radical. 4. Resolver la ecuación. 5. Comprobar.

  3. a) x + 1 + = 3 3x + 4 – 5 = 0 13 – 3x b) + 7x – 12 Ejercicio 1 Resuelve las siguientes ecuaciones: ¿x?

  4. x + 1 + = 9 3x + 4 = 8 – x 3x + 4 a) x + 1 + = 3 3x + 4 2 = 8 – x 3x + 4 3x + 4 = 64 – 16x + x2 x2 – 19x + 60 = 0 (x – 15)(x – 4) = 0 x1 – 15 = 0 ó x2 – 4 = 0 x1 = 15 x2 = 4

  5. S = { 4 } 15 + 1 + MI: 3·15 + 4 Comparación: ≠ 3 = 16 + 7 23 = 23 = 16 + 49 MI: = 5 + 16 4 + 1 + 3·4 + 4 = 5 + 4 = 9 = 3 Comprobación para x1 = 15 MD: 3 para x2 = 4 MD: 3 Comparación: 3 = 3

  6. b) 7x – 12 = 5 – 13 – 3x 13 – 3x 7x – 12 = 25 – 10 +13 – 3x 10x – 50 = – 10 13 – 3x : (10) 13 – 3x x – 5 = – – 5 = 0 13 – 3x + 7x – 12 2 2 2 2 x2 – 10x + 25 = 13 – 3x x2 – 7x + 12 = 0 (x – 4)(x – 3) = 0 ó x2 – 3 = 0 x1 – 4 = 0 x1 = 4 x2 = 3

  7. – 5 13 – 3·4 MI: + 7·4 – 12 = 16 + 1 – 5 = 28 – 12 + 13 – 12 – 5 – 5 13 – 3·3 + 7·3 – 12 MI: = 21 – 12 + 13 – 9 – 5 S = { 3; 4 } Comprobación para x1= 4 = 4 – 4 = 0 Comparación: 0 = 0 MD: 0 para x2= 3 = 3 + 2 – 5 = 0 MD: 0 Comparación: 0 = 0

  8. 2 2 = 15x + 4 5x + 1 + 4x – 3 4x – 3 + 2 20x2 –11x–3 + 5x +1 = 15x + 4 2 20x2 –11x– 3 = 6x + 6 20x2 –11x–3 = 3x + 3 11 x2= 4 : 2 = 15x + 4 5x + 1 + 4x – 3 20x2–11x – 3 = 9x2 + 18 x + 9 11x2 – 29x – 12 = 0 (11x + 4)(x – 3) = 0 ó 11x2 + 4 = 0 x1 – 3 = 0 x1= 3

  9. Comprobación : 4.3 – 3 + 5.3 + 1 15.3 + 4 11 11 x2= 4 4 4 ( ) – 3 = – 14 √ √ S = { 3 } x1 = 3 M.I: = 3 + 4 = 7 = 7 M.D: M.I = M.D Raíz extraña Imposible M.I:

  10. = 5x + 1 + 15x + 4 4x – 3   5x + 1 +  x – 3 A = Para el estudio individual 1. Resuelve las siguientes ecuaciones: S = {3} 2. Para qué valores de la variable, A toma el valor 2, si Respuesta: para x = 3

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