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air60549765
@air60549765
October 2021
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сократите дробь ( : - знак дроби )
9x^5-40x^3+16x : 3x^4 - 8x^3 + 4x^2
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sedinalana
Verified answer
9x^5-40x³+16x=x(9x^4-40x²+16)=9x(x²-4/9)(x²+32/9)=x(x-2/3)(x+2/3)(9x²+32)
9x^4-40x²+16=9(x²-4/9)(x²+32/9)
x²=a
9a²-40a+16=0
D=1600-576=1024
a1=(40-32)/18=4/9 U a2=((40+32)/18=32/9
3x^4-8x³+4x²=x²(3x²-8x+4)=3x(x-2/3)(x-2)
D=64-48=16
x1=(8-4)/6=2/3 U x2=(8+4)/6=2
(9x^5-40x³+16x)/(3x^4-8x³+4x²)=x(x-2/3)(x+2/3)(9x²+32)/3x²(x-2/3)(x-2)=
=(3x+2)(9x²+32)/9x(x-2)
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Answers & Comments
Verified answer
9x^5-40x³+16x=x(9x^4-40x²+16)=9x(x²-4/9)(x²+32/9)=x(x-2/3)(x+2/3)(9x²+32)9x^4-40x²+16=9(x²-4/9)(x²+32/9)
x²=a
9a²-40a+16=0
D=1600-576=1024
a1=(40-32)/18=4/9 U a2=((40+32)/18=32/9
3x^4-8x³+4x²=x²(3x²-8x+4)=3x(x-2/3)(x-2)
D=64-48=16
x1=(8-4)/6=2/3 U x2=(8+4)/6=2
(9x^5-40x³+16x)/(3x^4-8x³+4x²)=x(x-2/3)(x+2/3)(9x²+32)/3x²(x-2/3)(x-2)=
=(3x+2)(9x²+32)/9x(x-2)