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9.5E: Mazoezi

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    176498

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    Mazoezi hufanya kamili

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

    Katika mazoezi yafuatayo, tatua.

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

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

    Zoezi\(\PageIndex{12}\) writing exercises
    1. Eleza jinsi ya kutambua equation katika fomu quadratic.
    2. Eleza utaratibu wa kutatua equation katika fomu ya quadratic.
    Jibu

    1. Majibu yatatofautiana.

    Self Check

    Baada ya kukamilisha mazoezi, tumia orodha hii ili kutathmini ujuzi wako wa malengo ya sehemu hii.

    Jedwali hili linatoa orodha ya kutathmini ustadi wa malengo ya sehemu hii. Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations katika fomu quadratic. € â € â € kwa ujasiri, â € â € â € na baadhi ya msaada, â € au â € no, mimi donâ €™ t kupata hiyo.â €
    Kielelezo 9.4.43

    b Kwa kiwango cha 1-10, ungewezaje kupima ujuzi wako wa sehemu hii kwa kuzingatia majibu yako kwenye orodha? Unawezaje kuboresha hii?