f(x)=(x-a)(x-b)(x+1)-3,已知f(1)=1
證明(a-1)(b-1)=2
math题
2007-07-09 10:29 pm
回答 (3)
2007-07-09 10:38 pm
✔ 最佳答案
(1-a) (1-b) (1+1) - 3 = 1(1-a) (1-b) = 2
[-(a-1)] [-(b-1)] = 2
(a-1) (b-1) = 2
參考: by HKU student (me)
2007-07-10 3:57 am
f(x)=(x-a)(x-b)(x+1)-3
f(1)=1
(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)=4
(1-a)(1-b)X2=4
(1-a)(1-b)=2
-[(a-1)(b-1)]=-2
(a-1)(b-1)=2
f(1)=1
(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)=4
(1-a)(1-b)X2=4
(1-a)(1-b)=2
-[(a-1)(b-1)]=-2
(a-1)(b-1)=2
2007-07-10 1:50 am
f(x)=(x-a)(x-b)(x+1)-3
Sub 1 into x,
f(1)=(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)-3+3=1+3 (Add both sides by 3)
2(1-a)(1-b)=4
2(1-a)(1-b)/2=4/2 (Divide both sides by 2)
(1-a)(1-b)=2
(1-a)(1-b)/-1=2/-1 (Divide both sides by -1)
-(1-a)(1-b)= -2
(a-1)(1-b)= -2
(a-1)(1-b)/-1= -2/-1 (Divide both sides by -1)
(a-1)(b-1)=2
so (a-1)(b-1)=2
Sub 1 into x,
f(1)=(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)-3=1
(1-a)(1-b)(1+1)-3+3=1+3 (Add both sides by 3)
2(1-a)(1-b)=4
2(1-a)(1-b)/2=4/2 (Divide both sides by 2)
(1-a)(1-b)=2
(1-a)(1-b)/-1=2/-1 (Divide both sides by -1)
-(1-a)(1-b)= -2
(a-1)(1-b)= -2
(a-1)(1-b)/-1= -2/-1 (Divide both sides by -1)
(a-1)(b-1)=2
so (a-1)(b-1)=2
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