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NichaKatya
@NichaKatya
July 2022
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помогите решить неравенство
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m11m
х²-1
≥0
х²-5х+6
Разложим знаменатель на множители:
х²-5х+6=0
Д=25-24=1
х₁=(5-1)/2=4/2=2
х₂=6/2=3
х²-5х+6=(х-2)(х-3)
(х-1)(х+1)
≥0
(х-2)(х-3)
Используем метод интервалов:
(х-1)(х+1)(х-2)(х-3)≥0
х=1 х=-1 х=2 х=3
+ - + - +
----- -1(закрашено) -------- 1(закр) ------- 2(незакр)------ 3(незакр)-------
\\\\\\ \\\\\\\\\\ \\\\\\\\\\
х∈(-∞; -1]∨[1; 2)∨(3; ∞)
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Answers & Comments
х²-5х+6
Разложим знаменатель на множители:
х²-5х+6=0
Д=25-24=1
х₁=(5-1)/2=4/2=2
х₂=6/2=3
х²-5х+6=(х-2)(х-3)
(х-1)(х+1)≥0
(х-2)(х-3)
Используем метод интервалов:
(х-1)(х+1)(х-2)(х-3)≥0
х=1 х=-1 х=2 х=3
+ - + - +
----- -1(закрашено) -------- 1(закр) ------- 2(незакр)------ 3(незакр)-------
\\\\\\ \\\\\\\\\\ \\\\\\\\\\
х∈(-∞; -1]∨[1; 2)∨(3; ∞)