Mipango

Mifano ya hisabati iliyotatuliwa

Milinganyo ya kipeo cha pili: mifano iliyotatuliwa

Mifano iliyotatuliwa ya Milinganyo ya kipeo cha pili, kuanzia rahisi hadi ngumu, kila hatua ikiwa imeandikwa. Jaribu kila mmoja mwenyewe kwanza, kisha linganisha na suluhisho.

✓ Kila jibu hapa limekokotolewa na kukaguliwa na injini ya hisabati

Rahisi

  1. Mfano 1. Tatua x2+6x=0x^{2} + 6x = 0.

    1. Weka vigawo.
      (x)(x+6)=0(x)(x + 6) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=0 or x=−6x = 0 \text{ or } x = -6

    Jibu: x=0 or x=−6x = 0 \text{ or } x = -6

  2. Mfano 2. Tatua x2=16x^2 = 16.

    1. Chukua kipeuo pande zote mbili.
      x=±16=±4x = \pm\sqrt{16} = \pm 4

    Jibu: x=±4x = \pm 4

  3. Mfano 3. Tatua x2−11x=0x^{2} - 11x = 0.

    1. Weka vigawo.
      (x)(x−11)=0(x)(x - 11) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=0 or x=11x = 0 \text{ or } x = 11

    Jibu: x=0 or x=11x = 0 \text{ or } x = 11

Wastani

  1. Mfano 4. Tatua x2+3x−4=0x^{2} + 3x - 4 = 0.

    1. Weka vigawo.
      (x−1)(x+4)=0(x - 1)(x + 4) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=1 or x=−4x = 1 \text{ or } x = -4

    Jibu: x=1 or x=−4x = 1 \text{ or } x = -4

  2. Mfano 5. Tatua x2+13x+36=0x^{2} + 13x + 36 = 0.

    1. Weka vigawo.
      (x+9)(x+4)=0(x + 9)(x + 4) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=−9 or x=−4x = -9 \text{ or } x = -4

    Jibu: x=−9 or x=−4x = -9 \text{ or } x = -4

  3. Mfano 6. Tatua x2−13x+40=0x^{2} - 13x + 40 = 0.

    1. Weka vigawo.
      (x−5)(x−8)=0(x - 5)(x - 8) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=5 or x=8x = 5 \text{ or } x = 8

    Jibu: x=5 or x=8x = 5 \text{ or } x = 8

Ngumu

  1. Mfano 7. Tatua 3x2−8x=03x^{2} - 8x = 0.

    1. Weka vigawo.
      (3x−8)(x)=0(3x - 8)(x) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=83 or x=0x = \frac{8}{3} \text{ or } x = 0

    Jibu: x=83 or x=0x = \frac{8}{3} \text{ or } x = 0

  2. Mfano 8. Tatua 2x2−5x−42=02x^{2} - 5x - 42 = 0.

    1. Weka vigawo.
      (2x+7)(x−6)=0(2x + 7)(x - 6) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=−72 or x=6x = -\frac{7}{2} \text{ or } x = 6

    Jibu: x=−72 or x=6x = -\frac{7}{2} \text{ or } x = 6

  3. Mfano 9. Tatua 12x2−9x−81=012x^{2} - 9x - 81 = 0.

    1. Weka vigawo.
      (4x+9)(3x−9)=0(4x + 9)(3x - 9) = 0
    2. Weka kila kigawo kuwa sifuri.
      x=−94 or x=3x = -\frac{9}{4} \text{ or } x = 3

    Jibu: x=−94 or x=3x = -\frac{9}{4} \text{ or } x = 3

Zamu yako

Fanya mazoezi kwa maswali mapya ya aina hiyo hiyo. Utapata vidokezo, suluhisho kamili na kusahihisha papo hapo.

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