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lililiam
@lililiam
July 2022
1
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Выполните действия.
a)x²-x-6/4x+4*x+1/x²-6x+9
b)2d+8/d²+5d+6:d²-4/d²-4
c)x³+5x²-x-5/x²-25:(x+1)
d)n³-m³/n²-m²*n²+2nm+m²/n²+nm+m²
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nod1nodar
(x+1)²(x²+2x)=12
(x²+2x+1)(x²+2x)=12
x⁴+2x³+2x³+4x²+x²+2x=12
x⁴+4x³+5x²+2x-12=0
(x⁴-x³)+(5x³-5x²)+(10x²-10x)+(12x-12)=0
(x-1)(x³+5x²+10x+12)=0
x1=1
x³+5x²+10x+12=0
x³+3x²+2x²+6x+4x+12=0
(x³+3x²)+(2x²+6x)+(4x+12)=0
x²(x+3)+2x(x+3)+4(x+3)=0
(x+3)(x²+2x+4)=0
x2=-3
x²+2x+4=0
D = b2 - 4ac = 22 - 4·1·4 = 4 - 16 = -12 - нет действительных корней
Ответ: x1=1, x2=-3
второй вариант: (x+1)²(x²+2x)=12
x(x+1)²(x+2)=2*2*3 или = (-2)(-2)3 или
(-3)(-2)2
методом подбора находим x=1, x=-3
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Answers & Comments
(x²+2x+1)(x²+2x)=12
x⁴+2x³+2x³+4x²+x²+2x=12
x⁴+4x³+5x²+2x-12=0
(x⁴-x³)+(5x³-5x²)+(10x²-10x)+(12x-12)=0
(x-1)(x³+5x²+10x+12)=0
x1=1
x³+5x²+10x+12=0
x³+3x²+2x²+6x+4x+12=0
(x³+3x²)+(2x²+6x)+(4x+12)=0
x²(x+3)+2x(x+3)+4(x+3)=0
(x+3)(x²+2x+4)=0
x2=-3
x²+2x+4=0
D = b2 - 4ac = 22 - 4·1·4 = 4 - 16 = -12 - нет действительных корней
Ответ: x1=1, x2=-3
второй вариант: (x+1)²(x²+2x)=12
x(x+1)²(x+2)=2*2*3 или = (-2)(-2)3 или (-3)(-2)2
методом подбора находим x=1, x=-3