✔ 最佳答案
d=3-a-b-c 代入a^2+...=5
=> a^2+2b^2+3c^2+[(3-a-b)- c]^2=5
=> 4c^2 - 2(3-a-b)c + (3-a-b)^2+a^2+2b^2-5=0
(視為 c之一元2次方程式, c為實數根=>判別式>=0)
(3-a-b)^2- 4[(3-a-b)^2+a^2+2b^2-5] >=0
=>3(3-a-b)^2+4a^2+8b^2 -20 <=0
=> 11b^2- 6(3-a)b+3(3-a)^2+4a^2- 20 <=0
(視為 b之一元2次方程式, 圖形為拋物線開口向上, 欲<=0有實根, 判別式>=0)
=> 9(3-a)^2- 11[ 3(3-a)^2+4a^2- 20] >= 0
=> 24(3-a)^2 + 44a^2 - 220 <=0
=> 17a^2- 36a - 1 <=0
=> (18-√341)/17 <= a <= (18+√341)/17
註:答案有點難看,但願沒算錯!
2009-08-31 01:35:11 補充:
哇!算錯了,更正如下:
d=3-a-b-c代入a^2+...=5 => 9c^2-12(3-a-b)c+a^2+2b^2-5=0
判別式>=0 => 2(3-a-b)^2+a^2+2b^2-5 <=0
=> 4b^2 - 4(3-a)b+ 2(3-a)^2+a^5-5 <=0
判別式>=0 => a^2-3a+2 <=0
Ans: 1<= a <= 2