更新1:
(A)23 (B)33 (C)43 (D)53
已知m、n為一元二次方程式x²-3x-1=0的解，則m³+10n+20=?
回答 (2)
2016-02-14 9:15 am
✔ 最佳答案
因m為方程式的解, 故m² - 3m - 1 = 0 ⇒ m² = 3m+1, 又兩根和 = m + n = 3, 則 m³ + 10n + 20
= m(m²) + 10n + 20
= m(3m+1) + 10n + 20
= 3m²+m + 10n + 20
= 3(3m+1)+m + 10n + 20
= 10m + 10n + 23
= 10(m+n) + 23
= 10(3) + 23
= 53
答(D).
2016-02-14 9:35 am
x² - 3x - 1 = 0
m = (3 ±√13)/2 或 x = (3 ∓ √13)/2
m³ + 10n + 20
= [(3 ± √13)/2]³ + [10(3 ∓ √13)/2] + 20
= [(27 ± 27√13 + 117 ± 13√13)/8] + 15 ∓ 5√13 + 20
= 18 ± 5√13 + 15 ∓ 5√13 + 20
= 53
...... 答案選(D)
m = (3 ±√13)/2 或 x = (3 ∓ √13)/2
m³ + 10n + 20
= [(3 ± √13)/2]³ + [10(3 ∓ √13)/2] + 20
= [(27 ± 27√13 + 117 ± 13√13)/8] + 15 ∓ 5√13 + 20
= 18 ± 5√13 + 15 ∓ 5√13 + 20
= 53
...... 答案選(D)
收錄日期: 2021-04-18 14:27:23
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20160213234917AAC9XVj