數學題不等式

Note that x+3 >= 0 because √(x+3) is non-negative.
Also note that √(x+3) > (1/2)x is always true when x < 0

√(x+3) > (1/2)x
√(x+3) - (1/2)x > 0 or -3 <= x < 0
(√(x+3) - (1/2)x ) (√(x+3) + (1/2)x ) > 0 or -3 <= x < 0
x+3 - (1/4) x^2 > 0 or -3 <= x < 0
x^2 - 4x - 12 < 0 or -3 <= x < 0
(x - 6) (x + 2) < 0 or -3 <= x < 0
-2 < x < 6 or -3 <= x < 0
-3 <= x < 6

2007-06-06 14:05:22 補充：
First sentence should be:Note that x+3 >= 0 otherwise √(x+3) is undefined

2007-06-06 20:23:23 補充：
It's better to write:(-2 = -3x = -3-3

2007-06-06 20:24:09 補充：
It's better to write:(-2 < x < 6 or x < 0) and x >= -3x < 6 and x >= -3-3 <= x < 6

√(x+3) > (1/2)x
√(x+3) - (1/2)x > 0 or -3 <= x < 0
(√(x+3) - (1/2)x ) (√(x+3) + (1/2)x ) > 0 or -3 <= x < 0
x+3 - (1/4) x^2 > 0 or -3 <= x < 0
x^2 - 4x - 12 < 0 or -3 <= x < 0
(x - 6) (x + 2) < 0 or -3 <= x < 0
-2 < x < 6 or -3 <= x < 0
-3 <= x < 6

個答案應該係-2<6
√(x+3)>(1/2)x
x+3>(1/4)x^2
((1/2)x-3)((1/2)x+1)<0
(x-6)(x+2)<0
所以-2<6

2007-06-06 15:54:42 補充：
6 > X > -2

不等式√x+3>(1/2)x的解係咩
不知你的式是 √(x+3) > (1/2)x 還是 (√x)+3 >(1/2)x

若是
√(x+3) > (1/2)x，則
x + 3 > (1/4)x2
0 > x2 – 4x – 12
(x + 2)(x – 6) < 0
x > -2 及 x < 6
答案是 6 > X > -2

若是
(√x)+3 >(1/2)x
則
(√x) > (1/2)x – 3
x > [(1/2)x – 3]2
x > (1/4)x2 – 3x + 9
x > (1/4)x2 – 3x + 9
0 > x2 – 16 x + 36
用公式法解得
x < [16 + √(162 – 4*36)] / 2
= 8 + 2√7
及
x > [16 - √(162 – 4*36)] / 2
= 8 - 2√7
答案是 8 + 2√7 > x > 8 - 2√7