Question

Tseng

求解 謝謝

難 68. 已知n為正整數,且
10n+4<197<
10n+14
,
則n=
n+1
n+2
【中一中201】

Answer 1

✨ Jawaban Terbaik ✨

qn

左：
10n+4 < √97n + √97
(10-√97)n < √97 - 4
n < (√97 - 4)/(10 - √97)
= (√97 - 4)(10 + √97)/(100 - 97)
= (57+6√97)/3
= 19 + 2√97

右：
10n+14 > √97n + 2√97
(10-√97)n > 2√97 - 14
n > (2√97 - 14)/(10 - √97)
= (2√97 - 14)(10 + √97)/(100 - 97)
= (54 + 6√97)/3
= 18 + 2√97

合併：
18 + 2√97 < n < 19 + 2√97

2√97 = √388 = 19.⋯
37.⋯ < n < 38.⋯

⇒ n = 38