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9.5E：练习

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    练习成就完美

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

    在以下练习中，求解。

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

    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。 \(x=-2, x=\frac{4}{3}\)

    练习\(\PageIndex{12}\) writing exercises
    1. 解释如何识别二次形式的方程。
    2. 解释求解二次形式方程的程序。
    回答

    1。 答案会有所不同。

    自检

    a. 完成练习后，使用此清单评估您对本节目标的掌握程度。

    此表提供了一份清单，用于评估对本节目标的掌握程度。 选择你将如何回应 “我能以二次形式求解方程” 的说法。“自信地，” 在一些帮助下，“或者不，我不明白。™
    图 9.4.43

    b. 在 1-10 分中，根据你在清单上的回答，你会如何评价你对本节的掌握程度？ 你怎么能改善这个？

    This page titled 9.5E：练习 is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform.