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bacmandima
@bacmandima
July 2022
1
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Решить неравенство
log[tex] \frac{1}{2} [/tex] (x²-5x+6)>1
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m11m
Verified answer
ОДЗ: x²-5x+6>0
D=25-24=1
x₁=(5-1)/2=2
x₂=(5+1)/2=3
+ - +
------
2 ----------- 3
----------
\\\\\\\ \\\\\\\\\\\\
x∈(-∞; 2)U(3; +∞)
x² -5x+6 < (1/2)¹
x² -5x+6 -0.5 < 0
x² -5x +5.5 <0
D=25 - 22=3
x₁=(5-√3)/2 ≈ 1.63
x₂=(5+√3)/2≈ 3.36
+ - +
------ (5 - √3)/2
--------------
(5+√3)/2 ----------
\\\\\\\\\\\\\\\\\
x∈((5-√3)/2; (5+√3)/2)
С учетом ОДЗ получаем:
x∈((5-√3)/2; 2)U(3; (5+√3)/2)
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Answers & Comments
Verified answer
ОДЗ: x²-5x+6>0D=25-24=1
x₁=(5-1)/2=2
x₂=(5+1)/2=3
+ - +
------ 2 ----------- 3 ----------
\\\\\\\ \\\\\\\\\\\\
x∈(-∞; 2)U(3; +∞)
x² -5x+6 < (1/2)¹
x² -5x+6 -0.5 < 0
x² -5x +5.5 <0
D=25 - 22=3
x₁=(5-√3)/2 ≈ 1.63
x₂=(5+√3)/2≈ 3.36
+ - +
------ (5 - √3)/2 -------------- (5+√3)/2 ----------
\\\\\\\\\\\\\\\\\
x∈((5-√3)/2; (5+√3)/2)
С учетом ОДЗ получаем:
x∈((5-√3)/2; 2)U(3; (5+√3)/2)