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vjbcttfg1980
@vjbcttfg1980
October 2021
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Разложите на множители квадратный трехчлен А) 3х^2-24х+21 В) 1/6х^2+1/2х+1/3 2. Б) -9х^2+12 х-4 3.сократить 4х+4/3х^2+2х-1
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dasdasfa
Применяем формулу!
ax^2+bx+c=a(x-x1)(x-x2); x1; x2 -корни квадр. трёхчленa
a) 3x^2-24x+21=0
D1=12^2-3*21=144-63=81=9^2
x1=(12-9)/3=1; x2=(12+9)/3=7
3x^2-24x+21=3*(x-1)(x-7)
b) 1/6x^2+1/2x+1/3=0
x^2+3x+2=0
D=9-4*2*1=1; x1=-3-1) /2=-2; x2=(-3+1)/2=-1
1/6x^2+1/2x+1/3=1/6*(x+2)(x+1)
Б) -9x^2+12x-4=-(9x^2-12x+4)=-(3x-2)^2
(4x+4)/(3x^2+2x-1)=(4(x+1)) /(3(x+1)(x-1/3))=4/(3x-1)
так как 3x^2+2x-1=0
D1=1+3=4=2^2
x1=(-1-2)/3=-1; x2=(-1+2)/3=1/3
3x^2+2x-1=3(x+1)(x-1/3)=(x+1)(3x-1)
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Answers & Comments
ax^2+bx+c=a(x-x1)(x-x2); x1; x2 -корни квадр. трёхчленa
a) 3x^2-24x+21=0
D1=12^2-3*21=144-63=81=9^2
x1=(12-9)/3=1; x2=(12+9)/3=7
3x^2-24x+21=3*(x-1)(x-7)
b) 1/6x^2+1/2x+1/3=0
x^2+3x+2=0
D=9-4*2*1=1; x1=-3-1) /2=-2; x2=(-3+1)/2=-1
1/6x^2+1/2x+1/3=1/6*(x+2)(x+1)
Б) -9x^2+12x-4=-(9x^2-12x+4)=-(3x-2)^2
(4x+4)/(3x^2+2x-1)=(4(x+1)) /(3(x+1)(x-1/3))=4/(3x-1)
так как 3x^2+2x-1=0
D1=1+3=4=2^2
x1=(-1-2)/3=-1; x2=(-1+2)/3=1/3
3x^2+2x-1=3(x+1)(x-1/3)=(x+1)(3x-1)