Task/28556387
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Разложение квадратного трехчлена( по формуле и группировкой)
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* * * ax² +bx +c =a(x - x₁)(x - x₂) * * *
1.
x² +5x - 6 === x² - (- 6 +1)x +(-6)*1 ===
x² +5x - 6 =0 D =5² -4*1*(-6) = 25+24 =49 =7²
x₁ =( -5 -7)/2 = -6 ;
x₂ = (-5+7)/2 =1.
x² +5x - 6 =(x - x₁)(x - x₂) =(x -(-6) )(x -1) = (x+6)(x-1).
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x² +5x - 6 =x² +6x -x -6 =x(x+6) -(x+6) =(x+6)(x-1)
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3.
9x²+6x +1 * * * (3x +1)² = (3(x+1/3))² =3²(x+1/3)² =9(x+1/3)(x+1/3) * * *
9x²+6x +1 =0 D = 6² -4*9*1 =36 -36=0 или D₁ = (6/2)² -9*1 =9 -9=0 * * *
D = 0 ⇒ корни равны
x₁ =x₂ = -6/(2*9) = -1/3 * * * x₁ =x₂ =-3/9 =-1/3 * * *
9x²+6x +1 =9(x+1/3)(x+1/3) . * * * (3x +1)² * * *
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9x²+6x +1=9x²+3x +3x +1=3x(3x+1) +(3x+1) =(3x+1)(3x+1) = || (3x+1)² || =3(x+1/3)*3(x+1/3) =9(x+1/3)(x+1/3).
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5.
x² +x -2
x² +x -2 =0 D = 1² -4*1*(-2) =9 =3²
x₁ =( -1 -3)/2 = - 2 ;
x₂ = (-1+3)/2 =1.
x² +x -2 =(x-(-2))(x-1) = (x+2)(x-1).
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x² +x -2 = x² +2x -x -2 = x(x+2) -(x+2) =(x+2)(x-1).
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7.
x² - 5x - 6
x² - 5x - 6 =0 D =5² -4*1*(-6) =25 +24 =49 =7²
x₁ =( 5 -7)/2 = - 1 ;
x₂ = (5+7)/2 = 6.
x² - 5x - 6=(x -(-1))(x-6) =(x+1)(x-6) .
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x² - 5x - 6 =x² +x -6x -6 =x(x+1) -6(x+1) =(x+1)(x-6) .
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9.
x² - 5x + 6
x² - 5x + 6 =0 D =5² -4*1*6 =25 -24 =1²
x₁ =( 5 -1)/2 = 2 ;
x₂ = (5+1)/2 =3.
x² - 5x - 6=(x -2)(x-3) .
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x² - 5x - 6 =x² -2x -3x -6 =x(x-2) -3(x-2) =(x-2)(x-3).
Удачи !