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Hatug
@Hatug
July 2022
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сколько целых решений имеет неравенство: x(x+1)(x+2)(x+3)>=24
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sedinalana
Verified answer
[x(x+3)]*(x+1)(x+2)]≥24
(x²+3x)*(x²+3x+2)-24≥0
x²+3x=a
a(a+2)-24≥0
a²+2a-24≥0
a1+a1=-2 U a1*a2=-24
a1=-6⇒x²+3x=-6
x²+3x+6=0
D=9-24=-15 <0 нет решения
a2=4⇒x²+3x=4
x²+3x-4=0
x1+x2=-3 U x1*x2=-4
x1=-4 U x2=1
x∈(-∞;-4] U [1;∞)
Целых решений множество
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Answers & Comments
Verified answer
[x(x+3)]*(x+1)(x+2)]≥24(x²+3x)*(x²+3x+2)-24≥0
x²+3x=a
a(a+2)-24≥0
a²+2a-24≥0
a1+a1=-2 U a1*a2=-24
a1=-6⇒x²+3x=-6
x²+3x+6=0
D=9-24=-15 <0 нет решения
a2=4⇒x²+3x=4
x²+3x-4=0
x1+x2=-3 U x1*x2=-4
x1=-4 U x2=1
x∈(-∞;-4] U [1;∞)
Целых решений множество