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9.5E: Ejercicios

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    51775
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    La práctica hace a la perfección

    Ejercicio \(\PageIndex{11}\) Resolver ecuaciones en forma cuadrática

    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. \(15 x^{-2}-4 x^{-1}-4=0\)
    Responder

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

    Ejercicios de \(\PageIndex{12}\) escritura de ejercicios
    1. Explicar cómo reconocer una ecuación en forma cuadrática.
    2. Explicar el procedimiento para resolver una ecuación en forma cuadrática.
    Responder

    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 declaración “I puede resolver ecuaciones en forma cuadrática.†“Confidentemente, †“with algo de ayuda, †o “No, I don’ t get it.â€
    Figura 9.4.43

    b. En una escala de 1-10, ¿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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