Решить неравенство: [tex] log_{3} (x^{2} -4x) \leq log_{3} (x-6)[/tex]. Created by valeriyakustova. algebra-ru

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valeriyakustova @valeriyakustova

July 2022 1 15 Report

Решить неравенство:

[tex] log_{3} (x^{2} -4x) \leq log_{3} (x-6)[/tex]

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Evgenia4836

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ОДЗ:
x²-4x>0
x>6
x∈(-∞;0)∪(4;+∞) и (6;+∞)
объединяем и получаем одз x∈(6;+∞)

x²-4x≤x-6
x²-5x+6≤0
D=25-24=1
x1= (5+1)/2= 3
x2=(5-1)/2= 2
(x-3)(x-2)≤0
x∈[2;3] согласно ОДЗ решений нет. x∈∅

2 votes Thanks 1

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