✔ 最佳答案
圖片參考:
https://s.yimg.com/rk/AD06198854/o/1016380375.png
3.△ABC: AB=5,AC=6,BC=7,BM=AM,AD⊥BM,BD:DC=?
作AH⊥AC, x = AH, y = BHy^2 = 25 - x^2 = 49 - (6-x)^2=> x = 1=> y = √(25 - 1) = 2√6A = (0,0), M = (3,0), C = (6,0) => B = (1,2√6)
Line BM: y/(x-3) = 2√6/(-2) => y = -√6(x-3)
Line AD: y = x/√6
Line BC: y/(x-6) = 2√6/(-5) => y = -2√6(x-6)/5
Lines AD & BC: x/√6 = -2√6(x-6)/5 => x = 72/17=> y = x/√6 = 12√6/17=> D = (72/17, 12√6/17)=> BD = √[(72/17-1)^2 + (12√6/17-2√6)^2] = 77/17=> DC = √[(72/17-6)^2 + (12√6/17)^2] = 42/17=> BD/DC = 77/42 = 11/6
1.1.2.3.4.5.....2015中取出N個數,使得這N個數的任意三個數的和均為27的倍數,試求N的最大值?
[ ] = Gauss Function = Min Integer[2015 / 27] = [74.63]= 74 => 74*27= 1998
A1 = 1 + 2 + 24 + 0*27 = 1*27A2 = 1 + 2 + 24 + 1*27 = 2*27A3 = 1 + 2 + 24 + 2*27 = 3*27A4 = 1 + 2 + 24 + 3*27 = 4*27......A75 = 1 + 2 + 24 + 74*27 = 75*27A = {1,2,24,54,81,....,1998}=> Nmax = 75 + 2 {包括1 & 2} = 77
2. x,y = 實數,x > y > 0a = √x*y = √4*1 = 2 b = (x + y)/2 = (4 + 1)/2 = 非整數 => x,y必須同時 = Even or Odd
a = √(xy) = √(9*1) = 3b = (9 + 1)/2 = 5c = a^2/b = 9/5 = 非整數
a = √16 = √(8*2) = 4b = (8 + 2)/2 = 5c = a^2/b = 16/5 = 非整數.......
a = √(x*y) = √225 = √45*5 = 15b = (45 + 5)/2 = 25c = a^2/b = 225/25 = 9a + b + c = 15 + 25 + 9 = 49= O.K.=> ans: x = 45
4.a.b.c = 1~9不同整數,Min[(abc)/(a+b+c)] = ?
min = 1*2*3/(1+2+3) = 6/6 = 1
5. a.b.c > 0 (√2); a + b + c = 4 + 2 f(a,b,c) = (2b-c)/(a+b+2c) + (6a+8c)/(a+3b+c) - (a-2b)/(2a+b+c)
不論是算幾不等式 or 柯西不等式極點都存在於: a = b = c => min = f(a,a,a)
f = (2-1)/(1+1+2) + (6+8)/(1+3+1) - (1-2)/(2+1+1)= 1/4 + 14/5 + 1/4= 1/2 + 14/5= (5 + 28)/10= 3.3= min
2015-03-28 17:21:01 補充:
6.你話 N 有 77 個,包括 1,2,24,54,81,...,1998. 我數過,你的數字裡只有 76 個,不是 77 個。
Ans:
感恩匿名人老師指導 確實是76ㄍ
所以第1題答案改為 76