Решите неравенство: x^4-3x^3+2x^2/x^2-x-30 > 0. Created by dezdez. algebra-ru

x^2-x-30 > 0...

ВладимирБ

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Решение смотри в приложении

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sedinalana

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X^4-3x³+2x³=x²(x²-3x+2)=x²(x-2)(x-1)
x1+x2=3 U x1*x2=2⇒x1=2 U x2=1
x²-x-30=(x-6)(x+5)
x1+x2=1 U x1*x2=-30⇒x1=6 U x2=-5
------------------------------
(x^4-3x³+2x²)/(x²+x-30)>0
x²(x-2)(x-1)/(x-6)(x+5)>0
x=0 x=2 x=1 x=6 x=-5
+ _ _ + _ +
---------------(-5)-------------(0)--------------(1)----------(2)------------(6)----------------
x∈(-∞;-5) U (1;2) U (6;∞)

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