F.4 附加數學 - 絕對值 (高手請進)

｜x2 ＋ x － 13｜= 7
x2 ＋ x － 13 = 7 or x2 ＋ x － 13 = -7
x2 ＋ x － 20 = 0 or x2 ＋ x － 6 = 0
x= -5, -3, 2, 4



2｜x － 4｜= ｜7 － 3x｜
4(x-4)2 = (7-3x) 2
4x2-32x+64 = 9x2-42x+49
5x2-10x-15=0
x2-2x-3=0
x=3 or -1

1. |x^2 + x - 13| = 7
Case 1: x^2 + x - 13 = 7
=> x^2 + x - 20 = 0
=> (x + 5)(x - 4) = 0
=> x + 5 = 0 or x - 4 = 0
=> x = -5 or x = 4

Case 2: -(x^2 + x - 13) = 7
=> x^2 + x - 6 = 0
=> (x - 2)(x + 3) = 0
=> x = 2 or x = -3

In conclusion, for |x^2 + x - 13| = 7, x = -5, -3, 2 or 4.

2. 2|x - 4| = |7 - 3x|
Case 1: 2(x - 4) = (7 - 3x)
=> 5x = 15
=> x = 3

Case 2: 2(x - 4) = -(7 - 3x)
=> x = -1

In conclusion, for 2|x - 4| = |7 - 3x|, x = -1 or 3