Kopertina e librit Matematika 12

Zgjidhja e ushtrimit 3

Zgjidhja e ushtrimit 3 të mësimit 1.4A në librin Matematika 12 nga shtëpia botuese Botime Pegi me autorë Brian Jefferson, David Bowles, Eddie Mullan, Garry Wiseman, John Rayneau, Katie Wood, Mike Heylings, Paul Williams dhe Rob Wagner.

Pyetja

Zgjidhni ekuacionet e mëposhtme të fuqisë së dytë me anë të formulës. Shkruani përgjigjen e saktë (me rrënjë) dhe atë të përafërt, pas presjes dhjetore.

  1. 3x2+9x+5=03x^2 + 9x + 5 = 0
  2. 4x2+5x−1=04x^2 + 5x - 1 = 0
  3. x2+12x+5=0x^2 + 12x + 5 = 0
  4. 28−2x−x2=028 - 2x - x^2 = 0
  5. x2+15x−35=0x^2 + 15x - 35 = 0
  6. 34+3x−x2=034+ 3x - x^2 = 0
  7. 4x2+36x+81=04x^2 + 36x + 81 = 0
  8. 3x2−23x+21=03x^2 - 23x + 21 = 0
  9. 5x2+16x+9=05x^2 + 16x + 9 = 0
  10. 10x2−x−1=010x^2 - x - 1 = 0

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Zgjidhja

  1. 3x2+9x+5=0⇒x=−9±92−4×3×52×3=−9±216=−9±4.58266=−32±2163x^2 + 9x + 5 = 0 \rArr x = \dfrac{-9 \pm \sqrt{9^2 - 4 \times 3 \times 5}}{2 \times 3} = \dfrac{-9 \pm \sqrt{21}}{6} = \dfrac{-9 \pm 4.5826}{6} = -\dfrac{3}{2} \pm \dfrac{21}{6} ⇒\rArr x=−2.26x=-2.26 ose x=−0.74x=-0.74
  2. 4x2+5x−1=0⇒x=−5±52−4×4×(−1)2×4=−5±418=−5±6.40318=−58±4184x^2 + 5x - 1 = 0 \rArr x = \dfrac{-5 \pm \sqrt{5^2 - 4 \times 4 \times (-1)}}{2 \times 4} = \dfrac{-5 \pm \sqrt{41}}{8} = \dfrac{-5 \pm 6.4031}{8} = -\dfrac{5}{8} \pm \dfrac{\sqrt{41}}{8} ⇒\rArr x=0.18x=0.18 ose x=−1.43x=-1.43
  3. x2+12x+5=0⇒x=−12±122−4×1×52×1=−12±1242=−12±11.13552=−6±31x^2 + 12x + 5 = 0 \rArr x = \dfrac{-12 \pm \sqrt{12^2 - 4 \times 1 \times 5}}{2 \times 1} = \dfrac{-12 \pm \sqrt{124}}{2} = \dfrac{-12 \pm 11.1355}{2} = -6 \pm \sqrt{31} ⇒\rArr x=−0.43x=-0.43 ose x=−11.57x=-11.57
  4. 28−2x−x2=0⇒x=−(−2)±(−2)2−4×(−1)×282×(−1)=2±116−2=2±10.7703−2=−1±2928 - 2x - x^2 = 0 \rArr x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4 \times (-1) \times 28}}{2 \times (-1)} = \dfrac{2 \pm \sqrt{116}}{-2} = \dfrac{2 \pm 10.7703}{-2} = -1 \pm \sqrt{29} ⇒\rArr x=−6.39x=-6.39 ose x=4.39x=4.39
  5. x2+15x−35=0⇒−15±152−4×1×(−35)2×1=−15±3652=−15±19.1052=152±3652x^2 + 15x - 35 = 0 \rArr \dfrac{-15 \pm \sqrt{15^2 - 4 \times 1 \times (-35)}}{2 \times 1} = \dfrac{-15 \pm \sqrt{365}}{2} = \dfrac{-15 \pm 19.105}{2} = \dfrac{15}{2} \pm \dfrac{365}{2} ⇒\rArr x=2.05x=2.05 ose x=−17.05x=-17.05
  6. 34+3x−x2=0⇒x=−3±32−4×(−1)×342×(−1)=−3±145−2=−3±12.0416−2=32±145234 + 3x - x^2 = 0 \rArr x = \dfrac{-3 \pm \sqrt{3^2 - 4 \times (-1) \times 34}}{2 \times (-1)} = \dfrac{-3 \pm \sqrt{145}}{-2} = \dfrac{-3 \pm 12.0416}{-2} = \dfrac{3}{2} \pm \dfrac{\sqrt{145}}{2} ⇒\rArr x=−4.52x=-4.52 ose x=7.52x=7.52
  7. 4x2−36x+81=0⇒x=−(−36)±(−36)2−4×4×812×4=36±08=4.54x^2 - 36x + 81 = 0 \rArr x = \dfrac{-(-36) \pm \sqrt{(-36)^2 - 4 \times 4 \times 81}}{2 \times 4} = \dfrac{36 \pm \sqrt{0}}{8} = 4.5
  8. 3x2−23x+21=0⇒x=−(−23)±(−23)2−4×3×212×3=23±2776=23±16.64336=236±27763x^2 - 23x + 21 = 0 \rArr x = \dfrac{-(-23) \pm \sqrt{(-23)^2 - 4 \times 3 \times 21}}{2 \times 3} = \dfrac{23 \pm \sqrt{277}}{6} = \dfrac{23 \pm 16.6433}{6} = \dfrac{23}{6} \pm \dfrac{\sqrt{277}}{6} ⇒\rArr x=6.61x=6.61 ose x=1.06x=1.06
  9. 5x2+16x+9=0⇒x=−16±162−4×5×92×5=−16±7610=−16±8.717810=−85±1955x^2 + 16x + 9 = 0 \rArr x = \dfrac{-16 \pm \sqrt{16^2 - 4 \times 5 \times 9}}{2 \times 5} = \dfrac{-16 \pm \sqrt{76}}{10} = \dfrac{-16 \pm 8.7178}{10} = -\dfrac{8}{5} \pm \dfrac{\sqrt{19}}{5} ⇒\rArr x=−0.73x=-0.73 ose x=−2.47x=-2.47
  10. 10x2−x−1=0⇒x=−(−1)±(−1)2−4×10×(−1)2×10=1±4120=1±6.403120=120±412010x^2 - x - 1 = 0 \rArr x = \dfrac{-(-1) \pm \sqrt{(-1)^2 - 4 \times 10 \times (-1)}}{2 \times 10} = \dfrac{1 \pm \sqrt{41}}{20} = \dfrac{1 \pm 6.4031}{20} = \dfrac{1}{20} \pm \dfrac{\sqrt{41}}{20} ⇒\rArr x=0.37x=0.37 ose x=−0.27x=-0.27