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9.3E: Mazoezi

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    176585

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    Mazoezi hufanya kamili

    Mazoezi 1 - 4: Kukamilisha Square ya kujieleza Binomial

    Katika mazoezi yafuatayo, jaza mraba ili kufanya trinomial kamili ya mraba. Kisha kuandika matokeo kama mraba wa binomial.

      1. \(m^{2}-24 m\)
      2. \(x^{2}-11 x\)
      3. \(p^{2}-\frac{1}{3} p\)
      1. \(n^{2}-16 n\)
      2. \(y^{2}+15 y\)
      3. \(q^{2}+\frac{3}{4} q\)
      1. \(p^{2}-22 p\)
      2. \(y^{2}+5 y\)
      3. \(m^{2}+\frac{2}{5} m\)
      1. \(q^{2}-6 q\)
      2. \(x^{2}-7 x\)
      3. \(n^{2}-\frac{2}{3} n\)
    Jibu

    1. a.\((m-12)^{2}\) b.\(\left(x-\frac{11}{2}\right)^{2}\) c.\(\left(p-\frac{1}{6}\right)^{2}\)

    3. a.\((p-11)^{2}\) b.\(\left(y+\frac{5}{2}\right)^{2}\) c.\(\left(m+\frac{1}{5}\right)^{2}\)

    Mazoezi 5 - 28: Tatua Ulinganisho wa Quadratic wa Fomu\(x^{2}+b x+c=0\) by Completing the Square

    Katika mazoezi yafuatayo, tatua kwa kukamilisha mraba.

    5. \(u^{2}+2 u=3\)

    6. \(z^{2}+12 z=-11\)

    7. \(x^{2}-20 x=21\)

    8. \(y^{2}-2 y=8\)

    9. \(m^{2}+4 m=-44\)

    10. \(n^{2}-2 n=-3\)

    11. \(r^{2}+6 r=-11\)

    12. \(t^{2}-14 t=-50\)

    13. \(a^{2}-10 a=-5\)

    14. \(b^{2}+6 b=41\)

    15. \(x^{2}+5 x=2\)

    16. \(y^{2}-3 y=2\)

    17. \(u^{2}-14 u+12=-1\)

    18. \(z^{2}+2 z-5=2\)

    19. \(r^{2}-4 r-3=9\)

    20. \(t^{2}-10 t-6=5\)

    21. \(v^{2}=9 v+2\)

    22. \(w^{2}=5 w-1\)

    23. \(x^{2}-5=10 x\)

    24. \(y^{2}-14=6 y\)

    25. \((x+6)(x-2)=9\)

    26. \((y+9)(y+7)=80\)

    27. \((x+2)(x+4)=3\)

    28. \((x-2)(x-6)=5\)

    Jibu

    5. \(u=-3, u=1\)

    7. \(x=-1, x=21\)

    9. \(m=-2 \pm 2 \sqrt{10} i\)

    11. \(r=-3 \pm \sqrt{2} i\)

    13. \(a=5 \pm 2 \sqrt{5}\)

    15. \(x=-\frac{5}{2} \pm \frac{\sqrt{33}}{2}\)

    17. \(u=1, u=13\)

    19. \(r=-2, r=6\)

    21. \(v=\frac{9}{2} \pm \frac{\sqrt{89}}{2}\)

    23. \(x=5 \pm \sqrt{30}\)

    25. \(x=-7, x=3\)

    27. \(x=-5, x=-1\)

    Mazoezi 29 - 40: Tatua Ulinganisho wa Quadratic wa Fomu\(a x^{2}+b x+c=0\) by Completing the Square

    Katika mazoezi yafuatayo, tatua kwa kukamilisha mraba.

    29. \(3 m^{2}+30 m-27=6\)

    30. \(2 x^{2}-14 x+12=0\)

    31. \(2 n^{2}+4 n=26\)

    32. \(5 x^{2}+20 x=15\)

    33. \(2 c^{2}+c=6\)

    34. \(3 d^{2}-4 d=15\)

    35. \(2 x^{2}+7 x-15=0\)

    36. \(3 x^{2}-14 x+8=0\)

    37. \(2 p^{2}+7 p=14\)

    38. \(3 q^{2}-5 q=9\)

    39. \(5 x^{2}-3 x=-10\)

    40. \(7 x^{2}+4 x=-3\)

    Jibu

    29. \(m=-11, m=1\)

    31. \(n=1 \pm \sqrt{14}\)

    33. \(c=-2, c=\frac{3}{2}\)

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

    37. \(p=-\frac{7}{4} \pm \frac{\sqrt{161}}{4}\)

    39. \(x=\frac{3}{10} \pm \frac{\sqrt{191}}{10} i\)

    Mazoezi 41 - 42: mazoezi ya kuandika

    41. Kutatua equation\(x^{2}+10 x=-25\)

    1. kwa kutumia Mizizi ya Mizizi ya Mraba
    2. kwa Kukamilisha Square
    3. Ni njia ipi unayopendelea? Kwa nini?

    42. Tatua equation\(y^{2}+8y=48\) kwa kukamilisha mraba na kuelezea hatua zako zote.

    Jibu

    41. 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 kukamilisha mraba wa kujieleza binomial.â € â € kwa ujasiri, â € â € â € kwa msaada fulani, â € au â€no, mimi donâ €™ t kupata hiyo.â € Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations quadratic ya fomu x squared pamoja na b mara x pamoja c sawa 0 na kukamilisha mraba.â € € kwa uaminifu, â € € € kwa msaada fulani, â € au â € hakuna, mimi donâ €™ t kupata.â € Chagua jinsi gani unaweza kujibu kauli â € naweza kutatua equations quadratic ya fomu mara x squared pamoja na b mara x pamoja c sawa 0 kwa kukamilisha mraba.â € € kwa ujasiri, â € € € kwa msaada fulani, â € au â €hakuna, Mimi donâ €™ kupata hiyo.â €
    Kielelezo 9.2.103

    b Baada ya kuchunguza orodha hii, utafanya nini ili uwe na ujasiri kwa malengo yote?