it is given that f (x)= ( x+2) ( x-2)+ax+b
if f (2)=2 and f (-2)=4
find the values of a and b
sorry for waste your time,,
THZ,,
中四數學,,
2007-10-03 4:23 am
回答 (3)
2007-10-03 4:43 am
✔ 最佳答案
f(x)=(x+2)(x-2)+ax+b代f(2)=2,則
f(2)=(2+2)(2-2)+a(2)+b=2
0+2a+b=2--------"1"
代f(-2)=4,則
f(-2)=(-2+2)(-2-2)+a(-2)+b=4
0-2a+b=4-----------"2"
將"1"&"2"用simultaneous equation(聯立方程)計算
2a+b=2----"1"
+) -2a+b=4----"2"
2b =6
b =3
將b=3代入"1" or"2"
(代入"1")2a+(3)=2
2a =-1
a = -1/2 or -0.5
參考: me...
2007-10-03 4:31 am
f (-2)=4
2007-10-03 4:27 am
f(2) = (2+2)(2-2)+2a+b = 2, i.e. 2a+b = 2 ...(1)
f(-2) = (-2+2)(-2-2) +a(-2)+b = 4, i.e. -2a+b=4 ...(2)
(1)+(2): 2b = 6, b = 3
a = (2-3)/2 = -1/2
Therefore, a = -1/2 and b = 3
f(-2) = (-2+2)(-2-2) +a(-2)+b = 4, i.e. -2a+b=4 ...(2)
(1)+(2): 2b = 6, b = 3
a = (2-3)/2 = -1/2
Therefore, a = -1/2 and b = 3
參考: me
收錄日期: 2021-04-13 18:12:26
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https://hk.answers.yahoo.com/question/index?qid=20071002000051KK03468