若 [x] 表示不大於 x 的最大整數，解方程
(1) x/2 + 21 = 3[x]
(2) ([x])^2 = x + 3
數學知識交流 － 解取整方程 (2)
2012-04-28 6:01 am
回答 (1)
2012-04-28 11:49 pm
✔ 最佳答案
Let x=n+d where n is an integer and 1>d≥0(1) x/2+21=3[x]=>(n+d)/2+21=3n=>d=5n-42 is an integer ∴=0=>n=8.4 (contradiction)Therefore there is no solution(2) [x]^2=x+3=>n^2=n+d+3d=n^2-n-3 is an integer∴=0n^2-n-3=0=>n=2.3 or n=-1.3 both rejectedTherefore there is no solution
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