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honey14
@honey14
November 2021
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ПОМОГИТЕ, ЗАДАНИЕ 6.54
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A>0, (a+4)/2+(a+9)/2>5√a ⇔(2a+13)/2 >5√a
[(2a+13)/2 ]²>(5√a ) ²
(4a²+52a+169)/4 >(25a ) ⇔(4a²+52a+169)>100a
(4a²+52a-100a+169)>0 ⇔ (4a²-48a+169)>0 D=48²-4·4·169=2304-2704<0
⇔4a²-48a+169>0 ДЛЯ ВСЕХ a
Т.О (a+4)/2+(a+9)/2>5√a
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Answers & Comments
Verified answer
A>0, (a+4)/2+(a+9)/2>5√a ⇔(2a+13)/2 >5√a[(2a+13)/2 ]²>(5√a ) ²
(4a²+52a+169)/4 >(25a ) ⇔(4a²+52a+169)>100a
(4a²+52a-100a+169)>0 ⇔ (4a²-48a+169)>0 D=48²-4·4·169=2304-2704<0
⇔4a²-48a+169>0 ДЛЯ ВСЕХ a
Т.О (a+4)/2+(a+9)/2>5√a