Kopertina e librit Matematika 12

Zgjidhja e ushtrimit 3

Zgjidhja e ushtrimit 3 të mësimit 2A në librin Matematika 12 nga shtëpia botuese Mediaprint me autorë Greg Attwood, Jack Barraclough, Ian Bettison, Alistair Macpherson, Bronwen Moran, Su Nicholson, Diane Oliver, Joe Petran, Keith Bledger, Harry Smith, Geoff Staley, Robert Ward-Penny dhe Dave Wilkins.

Pyetja

Zgjidh ekuacionet që vijojnë:

  1. 3x2+5x=23x^2 + 5x = 2
  2. (2x−3)2=9(2x-3)^2 = 9
  3. (x−7)2=36(x-7)^2 = 36
  4. 2x2=82x^2 = 8
  5. 3x2=53x^2 = 5
  6. (x−3)2=13(x-3)^2 = 13
  7. (3x−1)2=11(3x-1)^2 = 11
  8. 5x2−10x2=−7+x+x25x^2 - 10x^2 = -7 + x + x^2
  9. 6x2−7=11x6x^2 - 7 = 11x
  10. 4x2+17x=6x−2x24x^2+17x=6x-2x^2

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Zgjidhja

  1. 3x2+5x−2=0⇒3x2−x+6x−2=0⇒x(3x−1)+2(3x−1)=0⇒(x+2)(3x−1)=0→x+2=0⇒x=−23x^2 +5x - 2 = 0 \rArr 3x^2 -x + 6x - 2 = 0 \rArr x(3x-1)+2(3x-1)=0 \rArr (x+2)(3x-1)=0 \to x+2=0 \rArr \boxed{x=-2} dhe 3x−1=0⇒3x=1⇒x=133x -1=0 \rArr 3x=1 \rArr \boxed{x=\dfrac{1}{3}}
  2. 4x2−12x+9=9⇒4x2−12x=0⇒4x(x−3)=0→4x=0⇒x=04x^2 - 12x + 9 = 9 \rArr 4x^2 - 12x = 0 \rArr 4x(x-3)=0 \to 4x=0 \rArr \boxed{x=0} dhe x−3=0⇒x=3x-3=0 \rArr \boxed{x=3}
  3. x2−14x+49=36⇒x2−14x+13=0⇒x2−x−13x+13=0⇒x(x−1)−13(x−1)=0⇒(x−13)(x−1)=0→x−13=0⇒x=13x^2 - 14x + 49 = 36 \rArr x^2 - 14x + 13 = 0 \rArr x^2 - x - 13x + 13 = 0 \rArr x(x-1)-13(x-1)=0 \rArr (x-13)(x-1)=0 \to x-13=0 \rArr \boxed{x=13} dhe x−1=0⇒x=1x-1=0 \rArr \boxed{x=1}
  4. x2=82⇒x2=4⇒x=4⇒x=±2x^2 = \dfrac{8}{2} \rArr x^2 = 4 \rArr x = \sqrt{4} \rArr \boxed{x= \pm2}
  5. x2=53⇒x=±53x^2 = \dfrac{5}{3} \rArr \boxed{x = \pm \sqrt{\dfrac{5}{3}}}
  6. (x−3)2=13⇒±(x−3)=13⇒x−3=±13→x−3=13⇒x=3+13\sqrt{(x-3)^2} = \sqrt{13} \rArr \pm(x-3)=\sqrt{13} \rArr x-3=\pm\sqrt{13} \to x-3=\sqrt{13} \rArr \boxed{x=3+\sqrt{13}} dhe x−3=−13⇒x=3−13x-3 = -\sqrt{13} \rArr \boxed{x=3-\sqrt{13}}
  7. (3x−1)2=11⇒±(3x−1)=11⇒3x−1=±11→3x−1=11⇒3x=1+11⇒x=1+113\sqrt{(3x-1)^2} = \sqrt{11} \rArr \pm (3x-1) = \sqrt{11} \rArr 3x-1 = \pm \sqrt{11} \to 3x-1=\sqrt{11} \rArr 3x = 1+\sqrt{11} \rArr \boxed{x=\dfrac{1+\sqrt{11}}{3}} dhe 3x−1=−11⇒3x=1−11⇒x=1−1133x - 1 = -\sqrt{11} \rArr 3x = 1 - \sqrt{11} \rArr \boxed{x=\dfrac{1-\sqrt{11}}{3}}
  8. −5x2=x2+x−7⇒−6x2−x+7=0⇒−6x2+6x−7x+7=0⇒−6x(x−1)−7(x−1)=0⇒(−6x−7)(x−1)=0→−6x−7=0⇒−6x=7⇒x=−76-5x^2 = x^2 + x - 7 \rArr -6x^2 - x + 7 = 0 \rArr -6x^2 + 6x - 7x + 7 = 0 \rArr -6x(x-1)-7(x-1)=0 \rArr (-6x-7)(x-1)=0 \to -6x-7=0 \rArr -6x=7 \rArr \boxed{x=-\dfrac{7}{6}} dhe x−1=0⇒x=1x-1=0 \rArr \boxed{x=1}
  9. 6x2−11x−7=0⇒6x2+3x−14x−7=0⇒3x(2x+1)−7(2x+1)=0⇒(3x−7)(2x+1)=0→3x−7=0⇒3x=7⇒x=736x^2 - 11x - 7 = 0 \rArr 6x^2 + 3x - 14x - 7 = 0 \rArr 3x(2x+1)-7(2x+1)=0 \rArr (3x-7)(2x+1)=0 \to 3x-7=0 \rArr 3x=7 \rArr \boxed{x=\dfrac{7}{3}} dhe 2x+1=0⇒2x=−1⇒x=−122x+1 = 0 \rArr 2x=-1 \rArr \boxed{x=-\dfrac{1}{2}}
  10. 4x2+2x2+17x−6x=0⇒6x2+11x=0⇒x(6x+11)=0→x=04x^2 + 2x^2 + 17x - 6x = 0 \rArr 6x^2 + 11x = 0 \rArr x(6x+11)=0 \to \boxed{x=0} dhe 6x+11=0⇒6x=−11⇒x=−1166x+11=0 \rArr 6x=-11 \rArr \boxed{x=-\dfrac{11}{6}}