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9.5E: Ejercicios

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    La práctica hace la perfección

    Ejercicio\(\PageIndex{11}\) Solve equations in quadratic form

    En los siguientes ejercicios, resuelve.

    1. \(x^{4}-7 x^{2}+12=0\)
    2. \(x^{4}-9 x^{2}+18=0\)
    3. \(x^{4}-13 x^{2}-30=0\)
    4. \(x^{4}+5 x^{2}-36=0\)
    5. \(2 x^{4}-5 x^{2}+3=0\)
    6. \(4 x^{4}-5 x^{2}+1=0\)
    7. \(2 x^{4}-7 x^{2}+3=0\)
    8. \(3 x^{4}-14 x^{2}+8=0\)
    9. \((x-3)^{2}-5(x-3)-36=0\)
    10. \((x+2)^{2}-3(x+2)-54=0\)
    11. \((3 y+2)^{2}+(3 y+2)-6=0\)
    12. \((5 y-1)^{2}+3(5 y-1)-28=0\)
    13. \(\left(x^{2}+1\right)^{2}-5\left(x^{2}+1\right)+4=0\)
    14. \(\left(x^{2}-4\right)^{2}-4\left(x^{2}-4\right)+3=0\)
    15. \(2\left(x^{2}-5\right)^{2}-5\left(x^{2}-5\right)+2=0\)
    16. \(2\left(x^{2}-5\right)^{2}-7\left(x^{2}-5\right)+6=0\)
    17. \(x-\sqrt{x}-20=0\)
    18. \(x-8 \sqrt{x}+15=0\)
    19. \(x+6 \sqrt{x}-16=0\)
    20. \(x+4 \sqrt{x}-21=0\)
    21. \(6 x+\sqrt{x}-2=0\)
    22. \(6 x+\sqrt{x}-1=0\)
    23. \(10 x-17 \sqrt{x}+3=0\)
    24. \(12 x+5 \sqrt{x}-3=0\)
    25. \(x^{\frac{2}{3}}+9 x^{\frac{1}{3}}+8=0\)
    26. \(x^{\frac{2}{3}}-3 x^{\frac{1}{3}}=28\)
    27. \(x^{\frac{2}{3}}+4 x^{\frac{1}{3}}=12\)
    28. \(x^{\frac{2}{3}}-11 x^{\frac{1}{3}}+30=0\)
    29. \(6 x^{\frac{2}{3}}-x^{\frac{1}{3}}=12\)
    30. \(3 x^{\frac{2}{3}}-10 x^{\frac{1}{3}}=8\)
    31. \(8 x^{\frac{2}{3}}-43 x^{\frac{1}{3}}+15=0\)
    32. \(20 x^{\frac{2}{3}}-23 x^{\frac{1}{3}}+6=0\)
    33. \(x-8 x^{\frac{1}{2}}+7=0\)
    34. \(2 x-7 x^{\frac{1}{2}}=15\)
    35. \(6 x^{-2}+13 x^{-1}+5=0\)
    36. \(15 x^{-2}-26 x^{-1}+8=0\)
    37. \(8 x^{-2}-2 x^{-1}-3=0\)
    38. \(15 x^{-2}-4 x^{-1}-4=0\)
    Contestar

    1. \(x=\pm \sqrt{3}, x=\pm 2\)

    3. \(x=\pm \sqrt{15}, x=\pm \sqrt{2} i\)

    5. \(x=\pm 1, x=\frac{ \pm \sqrt{6}}{2}\)

    7. \(x=\pm \sqrt{3}, x=\pm \frac{\sqrt{2}}{2}\)

    9. \(x=-1, x=12\)

    11. \(x=-\frac{5}{3}, x=0\)

    13. \(x=0, x=\pm \sqrt{3}\)

    15. \(x=\pm \frac{11}{2}, x=\pm \frac{\sqrt{22}}{2}\)

    17. \(x=25\)

    19. \(x=4\)

    21. \(x=\frac{1}{4}\)

    23. \(x=\frac{1}{25}, x=\frac{9}{4}\)

    25. \(x=-1, x=-512\)

    27. \(x=8, x=-216\)

    29. \(x=\frac{27}{8}, x=-\frac{64}{27}\)

    31. \(x=27, x=64,000\)

    33. \(x=1, x=49\)

    35. \(x=-2, x=-\frac{3}{5}\)

    37. \(x=-2, x=\frac{4}{3}\)

    Ejercicio\(\PageIndex{12}\) writing exercises
    1. Explicar cómo reconocer una ecuación en forma cuadrática.
    2. Explicar el procedimiento para resolver una ecuación en forma cuadrática.
    Contestar

    1. Las respuestas variarán.

    Autocomprobación

    a. después de completar los ejercicios, utilice esta lista de verificación para evaluar su dominio de los objetivos de esta sección.

    Esta tabla proporciona una lista de verificación para evaluar el dominio de los objetivos de esta sección. Elige cómo responderías a la afirmación “Puedo resolver ecuaciones en forma cuadrática.††œconfiadamente, †“with some help, †o †œno, I donâ €™ t get it.â€
    Figura 9.4.43

    b. En una escala del 1 al 10, ¿cómo calificaría su dominio de esta sección a la luz de sus respuestas en la lista de verificación? ¿Cómo se puede mejorar esto?

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