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Ririkoz
@Ririkoz
July 2022
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помогите пожалуйста, с объяснением задания:
log^2 0,5 X + log0,5 X - 2=<0
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Эксперт5
Verified answer
ОДЗ: x>0
a²+a-2≤0
(a+2)(a-1)≤0
+ - +
________[-2]_____________[1]_________
a∈[-2;1]
\left \{ {log_{0,5}x \geq -2} \atop {log_{0,5}x \leq 1}} \right. =\ \textgreater \ \left \{ {{log_{0,5}x \geq log_{0,5}4} \atop {log_{0,5}x \leq log_{0,5}0,5}} \right.\; \; \; \; \; \; 0\ \textless \ 0,5\ \textless \ 1\\\\ \left \{ {{x \leq 4} \atop {x \geq 0,5}} \right. [/tex]
Ответ: [0,5;4]
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Answers & Comments
Verified answer
ОДЗ: x>0
a²+a-2≤0
(a+2)(a-1)≤0
+ - +
________[-2]_____________[1]_________
a∈[-2;1]
\left \{ {log_{0,5}x \geq -2} \atop {log_{0,5}x \leq 1}} \right. =\ \textgreater \ \left \{ {{log_{0,5}x \geq log_{0,5}4} \atop {log_{0,5}x \leq log_{0,5}0,5}} \right.\; \; \; \; \; \; 0\ \textless \ 0,5\ \textless \ 1\\\\ \left \{ {{x \leq 4} \atop {x \geq 0,5}} \right. [/tex]
Ответ: [0,5;4]