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SECTION I: (50 MARKS) (Answer all the questions in this section)

Mathematics

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Answer

x=1x = 1

x=2x = 2

Step-by-step solution

6 steps

Hapa kuna hatua za kutatua swali hilo:

  1. Gawanya mlinganyo mzima kwa 2 ili kufanya mgawo wa x2x^2 kuwa 1.

    2x22−6x2+42=02\frac{2x^2}{2} - \frac{6x}{2} + \frac{4}{2} = \frac{0}{2} x2−3x+2=0x^2 - 3x + 2 = 0

  2. Hamisha nambari isiyobadilika (constant term) kwenda upande wa kulia wa mlinganyo.

    x2−3x=−2x^2 - 3x = -2

  3. Kamilisha mraba kwa kuongeza (−32)2(\frac{-3}{2})^2 kwa pande zote mbili za mlinganyo.

    x2−3x+(−32)2=−2+(−32)2x^2 - 3x + \left(\frac{-3}{2}\right)^2 = -2 + \left(\frac{-3}{2}\right)^2 x2−3x+94=−2+94x^2 - 3x + \frac{9}{4} = -2 + \frac{9}{4}

  4. Rahisisha upande wa kulia na andika upande wa kushoto kama mraba kamili.

    (x−32)2=−84+94\left(x - \frac{3}{2}\right)^2 = -\frac{8}{4} + \frac{9}{4} (x−32)2=14\left(x - \frac{3}{2}\right)^2 = \frac{1}{4}

  5. Chukua mzizi wa mraba wa pande zote mbili.

    x−32=±14x - \frac{3}{2} = \pm\sqrt{\frac{1}{4}} x−32=±12x - \frac{3}{2} = \pm\frac{1}{2}

  6. Tatua kwa xx.

    Kuna suluhisho mbili:

    x=32+12aux=32−12x = \frac{3}{2} + \frac{1}{2} \quad \text{au} \quad x = \frac{3}{2} - \frac{1}{2} x=42aux=22x = \frac{4}{2} \quad \text{au} \quad x = \frac{2}{2} x=2aux=1x = 2 \quad \text{au} \quad x = 1

    Thamani za xx ni:
    x=1x = \boxed{1} au x=2x = \boxed{2}

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