a 8 x 4 26 x 2 15 b 9 x 4 80 x 2 9 d 91 x 2 1 x 2 80 x 2 No tiene solución real

A 8 x 4 26 x 2 15 b 9 x 4 80 x 2 9 d 91 x 2 1 x 2 80

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a) 8 x 4 + 26 x 2 + 15 = 0 b) 9 x 4 + 80 x 2 9 = 0 d) 9(1 x 2 )(1 + x 2 ) + 80 x 2 = 0 No tiene solución real. z 2 = − 9 No tiene solución real. No tiene solución real. z 1 = 9 x 1 = − 3 x 2 = 3 z 2 = No tiene solución real. Obtén las soluciones de las ecuaciones. d) 2 3 9 1 2 2 x x = c) 8 x x x + = 12 20 3 b) 3 ( 2) x x x 2 2 2 2 3 = a) 2 ( 7 2 x x x x 3 2 12 6 = ) 067 1 9 z z z = ± = ± = = − 80 80 4 9 2 80 82 18 9 2 1 2 ( 9) ( 9) 1 9 d) 9(1 )(1 80 9 80 + + = + + = = x x x x x z x 2 2 2 4 2 0 9 0 2 ) ⎯⎯→ + + = 9 80 z z 2 9 0 z = − − ± = ± ( 5) ( 5) 6 2 4 6 2 2 5 23 12 c) 6 5 6 5 6 5 2 0 2 0 2 0 2 4 4 2 2 2 + = + = + = = x x x x z z z x ⎯⎯→ z x x 1 1 2 1 1 3 1 3 = = − = z z z = ± = ± = = − 80 80 4 9 2 9 80 82 18 1 9 9 2 1 2 ( 9) b) 9 80 9 80 x x z z z x 4 2 2 9 0 9 0 2 + = + = = ⎯⎯→ z z z = ± = ± = − = − 26 26 4 8 15 2 8 26 14 16 3 4 5 2 2 1 2 a) 8 26 8 26 x x z z z x 4 2 2 15 0 15 0 2 + + = + + = = ⎯⎯→ c) 6 5 2 0 2 4 + = x x 066
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75 z 1 = 9 x 1 = − 3 x 2 = 3 z 2 = 4 x 3 = − 2 x 4 = 2 z 1 = 1 x 1 = − 1 x 2 = 1 z 2 = No tiene solución real. No tiene solución real. Completa las siguientes ecuaciones escribiendo un número en el segundo miembro, de manera que tengan estas soluciones. b) 4 1 1 5 13 12 1 x x x + + = a) x x + + = − 7 2 4 1 3 b) 4 4 1 1 5 1 x x x x + + = = a) 4 x x x + + = = 7 2 1 2 068 z = − − ± = ± ( ) ( ) 2 2 4 6 9 2 6 2 212 12 2 d) 9 2 1 3 6 2 9 0 6 2 9 0 2 2 4 2 2 2 x x x x z z z x = + = + = = ⎯⎯→ 5 2 z z z = − ± = − ± = = − 3 3 4 2 5 2 2 3 7 4 1 5 2 2 1 2 ( ) c) 8 2 x x x x x z z z x + = + = + = = 12 20 3 5 0 2 3 5 0 3 4 2 2 2 ⎯⎯→ z x x 2 3 4 1 9 1 3 1 3 = = − = z x x 1 1 2 = = − = 2 2 2 z z z = − − ± = ± = = ( 19) ( 19) 2 1 2 4 9 2 2 9 19 17 18 2 1 9 b) 3 2) 9 19 x x x x x z z x 2 2 2 4 2 2 2 3 9 19 2 0 2 ( = + = = ⎯⎯→ z + = 2 0 z z z = − − ± = ± = = ( 13) ( 13) 2 1 2 4 1 36 2 1 13 5 2 9 4 a) 2 ( 7 ) 2 13 1 x x x x x x z z x 3 2 4 2 2 12 6 36 0 2 = + = = ⎯⎯→ 3 z + = 36 0 2 SOLUCIONARIO
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76 Resuelve y comprueba las soluciones. Estas ecuaciones tienen cero, una o dos soluciones. Determínalas. a) No tiene solución. b) Tiene dos soluciones: x 1 = 2 x 2 = 6 c) Tiene dos soluciones: x 1 = 2 x 2 = − 4 d) Tiene una solución: x = 4 e) No tiene solución. c) 3 x x x 2 8 0 + + = e) 2 x x + = 2 5 1 0 b) 3 x x = 2 2 2 d) 3 1 5 3 + = x x a) 4 2 1 3 3 5 0 x x + = 070 x = + = − − = 7 7 2 7 6 2 3 1 2 0 d) x x x x x x + = + = + + = 2 6 2 0 2 6 4 6 4 1 6 x = = 3 2 3 2 3 5 2 2 1 x = = = 9 2 9 2 9 5 4 4 1 x x x = − − ± = ± = = ( ) ( ) 12 12 4 1 27 2 1 12 6 2 9 3 2 1 2 c) 2 2 5 1 12 27 0 2 x x x x = + = x = + + = + 0 2 3 0 1 2 0 2 2 1 2 0 x = + + = + = 5 2 3 5 1 2 5 2 2 4 10 2 0
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