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Алкадиеныч
@Алкадиеныч
July 2022
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Решить неравенство
[tex] 25^{1.5+x} \ \textless \ =80* 5^{x+1} -275[/tex]
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sharadi
Verified answer
(5²)¹⁾⁵⁺ˣ ≤ 80*5ˣ⁺¹ - 275
5³ * 5ˣ ≤ 80*5ˣ⁺¹ - 275 |: 5
5²*5ˣ ≤ 16*5ˣ⁺¹ - 55
5ˣ = t
25t² -80t +55 ≤ 0
5t² -`16t +11 ≤ 0
t₁ = 1 5ˣ = 1, ⇒ х = 0
t₂ = 11/5 5ˣ = 11/3, ⇒ хlg5 = lg11 - lg5, ⇒ x = (lg11 - lg5)/lg5
-∞ 0 (lg11 - lg5)/lg5 +∞
+ - +
IIIIIIIIIIIIIIIIIIIIIIIIIII]
Ответ: х∈[0; (lg11 - lg5)/lg5]
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Answers & Comments
Verified answer
(5²)¹⁾⁵⁺ˣ ≤ 80*5ˣ⁺¹ - 2755³ * 5ˣ ≤ 80*5ˣ⁺¹ - 275 |: 5
5²*5ˣ ≤ 16*5ˣ⁺¹ - 55
5ˣ = t
25t² -80t +55 ≤ 0
5t² -`16t +11 ≤ 0
t₁ = 1 5ˣ = 1, ⇒ х = 0
t₂ = 11/5 5ˣ = 11/3, ⇒ хlg5 = lg11 - lg5, ⇒ x = (lg11 - lg5)/lg5
-∞ 0 (lg11 - lg5)/lg5 +∞
+ - +
IIIIIIIIIIIIIIIIIIIIIIIIIII]
Ответ: х∈[0; (lg11 - lg5)/lg5]