Kopertina e librit Matematika 10 - 11: Pjesa I

Zgjidhja e ushtrimit 10

Zgjidhja e ushtrimit 10 të mësimit 10.1A në librin Matematika 10 - 11: Pjesa I nga shtëpia botuese Botime Pegi me autorë Steve Fearnley, June Haighton, Steve Lomax, Peter Mullarkey, James Nicholson dhe Matt Nixon.

Pyetja

Zgjidhni ekuacionet e mëposhtme.

  1. (x+3)(x+4)=(x+7)(x−2)(x+3)(x+4)=(x+7)(x-2)
  2. (y−7)2=(y+5)2(y-7)^2=(y+5)^2

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Zgjidhja

  1. x×x+x×4+3×x+3×4=x×x+x×(−2)+7×x+7×(−2)⇒x2+4x+3x+12=x2−2x+7x−14⇒7x+12=5x−14⇒7x−5x=−14−12⇒2x=−26⇒x=−262=−13x \times x + x \times 4 + 3 \times x + 3 \times 4 = x \times x + x \times (-2) + 7 \times x + 7 \times (-2) \rArr \cancel{x^2}+4x+3x+12=\cancel{x^2}-2x+7x-14 \rArr 7x+12=5x-14 \rArr 7x-5x=-14-12 \rArr 2x=-26 \rArr x=\dfrac{-26}{2}=-13
  2. (y−7)(y−7)=(y+5)(y+5)⇒y×y+y×(−7)−7×y−7×(−7)=y×y+y×5+5×y+5×5⇒y2−7y−7y+49=y2+5y+5y+25⇒−14y+49=10y+25⇒49−25=10y+14y⇒24=24y⇒y=2424=1(y-7)(y-7)= (y+5)(y+5) \rArr y \times y+y\times(-7)-7\times y - 7 \times (-7) = y \times y + y \times 5 + 5\times y + 5 \times 5 \rArr \cancel{y^2}-7y-7y+49=\cancel{y^2}+5y+5y+25 \rArr -14y+49=10y+25 \rArr 49-25=10y+14y \rArr 24=24y \rArr y=\dfrac{24}{24}=1