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10.2E: Mazoezi

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    Mazoezi hufanya kamili

    Kukamilisha Square ya kujieleza Binomial

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

    Mfano\(\PageIndex{43}\)

    \(a^2+10a\)

    Jibu

    \((a+5)^2\)

    Mfano\(\PageIndex{44}\)

    \(b^2+12b\)

    Mfano\(\PageIndex{45}\)

    \(m^2+18m\)

    Jibu

    \((m+9)^2\)

    Mfano\(\PageIndex{46}\)

    \(n^2+16n\)

    Mfano\(\PageIndex{47}\)

    \(m^2−24m\)

    Jibu

    \((m−12)^2\)

    Mfano\(\PageIndex{48}\)

    \(n^2−16n\)

    Mfano\(\PageIndex{49}\)

    \(p^2−22p\)

    Jibu

    \((p−11)^2\)

    Mfano\(\PageIndex{50}\)

    \(q^2−6q\)

    Mfano\(\PageIndex{51}\)

    \(x^2−9x\)

    Jibu

    \((x−\frac{9}{2})^2\)

    Mfano\(\PageIndex{52}\)

    \(y^2+11y\)

    Mfano\(\PageIndex{53}\)

    \(p^2−13p\)

    Jibu

    \((p−16)^2\)

    Mfano\(\PageIndex{54}\)

    \(q^2+34q\)

    Tatua Ulinganisho wa Quadratic wa Fomu \(x^ 2 + b x + c = 0\) kwa Kukamilisha Mraba

    Katika mazoezi yafuatayo, tatua kwa kukamilisha mraba.

    Mfano\(\PageIndex{55}\)

    \(v^2+6v=40\)

    Jibu

    \(v=−10\),\(v=4\)

    Mfano\(\PageIndex{56}\)

    \(w^2+8w=65\)

    Mfano\(\PageIndex{57}\)

    \(u^2+2u=3\)

    Jibu

    \(u=−3\),\(u=1\)

    Mfano\(\PageIndex{58}\)

    \(z^2+12z=−11\)

    Mfano\(\PageIndex{59}\)

    \(c^2−12c=13\)

    Jibu

    \(c=−1\),\(c=13\)

    Mfano\(\PageIndex{60}\)

    \(d^2−8d=9\)

    Mfano\(\PageIndex{61}\)

    \(x^2−20x=21\)

    Jibu

    \(x=−1\),\(x=21\)

    Mfano\(\PageIndex{62}\)

    \(y^2−2y=8\)

    Mfano\(\PageIndex{63}\)

    \(m^2+4m=−44\)

    Jibu

    hakuna ufumbuzi halisi

    Mfano\(\PageIndex{64}\)

    \(n^2−2n=−3\)

    Mfano\(\PageIndex{65}\)

    \(r^2+6r=−11\)

    Jibu

    hakuna ufumbuzi halisi

    Mfano\(\PageIndex{66}\)

    \(t^2−14t=−50\)

    Mfano\(\PageIndex{67}\)

    \(a^2−10a=−5\)

    Jibu

    \(a=5\pm2\sqrt{5}\)

    Mfano\(\PageIndex{68}\)

    \(b^2+6b=41\)

    Mfano\(\PageIndex{69}\)

    \(u^2−14u+12=−1\)

    Jibu

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

    Mfano\(\PageIndex{70}\)

    \(z^2+2z−5=2\)

    Mfano\(\PageIndex{71}\)

    \(v^2=9v+2\)

    Jibu

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

    Mfano\(\PageIndex{72}\)

    \(w^2=5w−1\)

    Mfano\(\PageIndex{73}\)

    \((x+6)(x−2)=9\)

    Jibu

    \(x=−7\),\(x=3\)

    Mfano\(\PageIndex{74}\)

    \((y+9)(y+7)=79\)

    Tatua Ulinganisho wa Quadratic wa Fomu\(ax^2+bx+c=0\) kwa Kukamilisha Mraba

    Katika mazoezi yafuatayo, tatua kwa kukamilisha mraba.

    Mfano\(\PageIndex{75}\)

    \(3m^2+30m−27=6\)

    Jibu

    \(m=−11\),\(m=1\)

    Mfano\(\PageIndex{76}\)

    \(2n^2+4n−26=0\)

    Mfano\(\PageIndex{77}\)

    \(2c^2+c=6\)

    Jibu

    \(c=−2\),\(c=\frac{3}{2}\)

    Mfano\(\PageIndex{78}\)

    \(3d^2−4d=15\)

    Mfano\(\PageIndex{79}\)

    \(2p^2+7p=14\)

    Jibu

    \(p=−\frac{7}{4}\pm\frac{\sqrt{161}}{4}\)

    Mfano\(\PageIndex{80}\)

    \(3q^2−5q=9\)

    kila siku Math

    Mfano\(\PageIndex{81}\)

    Rafi anajenga uwanja wa michezo mstatili kuwa na eneo la futi za mraba 320. Anataka upande mmoja wa uwanja wa michezo uwe mrefu wa miguu minne kuliko upande mwingine. Tatua equation\(p^2+4p=320\) kwa p, urefu wa upande mmoja wa uwanja wa michezo. Urefu wa upande mwingine ni nini.

    Jibu

    Miguu 16, miguu 20

    Mfano\(\PageIndex{82}\)

    Yvette anataka kuweka bwawa la kuogelea la mraba kwenye kona ya mashamba yake. Yeye atakuwa na 3 mguu staha upande wa kusini wa pool na a 9 mguu staha upande wa magharibi wa pool. Ana jumla ya eneo la futi za mraba 1080 kwa bwawa na Decks mbili. Kutatua equation\((s+3)(s+9)=1080\) kwa s, urefu wa upande wa pool.

    Mazoezi ya kuandika

    Mfano\(\PageIndex{83}\)

    Kutatua equation\(x^2+10x=−2\)

    1. kwa kutumia Mizizi ya Mizizi ya Mraba na
    2. kwa kukamilisha mraba.
    3. Ni njia ipi unayopendelea? Kwa nini?
    Jibu
    1. -5
    2. -5
    3. Majibu yatatofautiana.
    ​​​​​​​
    Mfano\(\PageIndex{84}\)

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

    ​​​​​​​

    Self Check

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

    Jedwali hili lina safu nne na nguzo nne. Mstari wa kwanza ni mstari wa kichwa na huandika kila safu. Safu ya kwanza inaitwa “Naweza...”, pili “Kwa ujasiri”, ya tatu “Kwa msaada fulani” na ya mwisho “Hapana - Siipati”. Katika safu ya “Naweza...” safu inayofuata inasoma “kukamilisha mraba wa kujieleza kwa binomial.” Mstari unaofuata unasoma “kutatua equations quadratic ya fomu x squared pamoja b x pamoja c sawa na sifuri kwa kukamilisha mraba.” na mstari wa mwisho unasoma “kutatua equations quadratic ya fomu x squared pamoja b x plus c c sawa na sifuri kwa kukamilisha mraba.” Nguzo zilizobaki ni tupu.

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