中四附加數問題

1) x^2 - 4x + 2 + k ( x - 4)^2
x^2 - 4x + 2 + k(x^2 - 8x + 16)
(1+k)x^2 - (4+8k)x + (16k+2)
由於佢係non-negative , 所以 係冇real root 或者double root
delta = (4+8k)^2 - 4(1+k)(16k+2) <= 0
16 + 64k + 64k^2 - 64k^2 - 64k - 8 - 8k <= 0
-8k + 8 <= 0
k >= 0

2) y = 6x - 1 / 3x^2 - 2x + 1
y*(3x^2 - 2x + 1) = 6x - 1
3y(x^2) - (2y+6)x + (y + 1) = 0
delta = (2y + 6)^2 - 4(y+1)(3y) >= 0
4y^2 + 24y + 36 - 12y^2 - 12y >= 0
-8y^2 + 12 y + 36 >= 0
2y^2 - 3y - 9 <= 0
(2y + 3)(y - 3) <= 0
-2/3 <= y <= 3

2007-11-13 18:36:41 補充：
打錯,第2題個答案係-3/2 <= y <= 3 ^ ^

2007-11-13 18:46:44 補充：
"& It;"是<"& gt;"是>

1) x^2-4x+2+k(x-4)^2
=x^2-4x+2+kx^2-8kx+16k
=(1+k)x^2+(-4-8k)x+(2+16k)
由於x^2-4x+2+k(x-4)^2沒有實根
所以b^2-4ac〈0
(-4-8k)^2-4(1+k)(2+16k)〈0
16+64k+64k^2-8-64k-8k-64k^2〈0
8-8k<0
所以 k>1