3^x-2y=9^x+1
5^x-y=125
指數函數 解聯合方程
2012-05-19 5:21 am
回答 (2)
2012-05-19 7:42 am
✔ 最佳答案
3^(x-2y) = 9^(x+1) .... (1)5^(x-y) = 125 ... (2)
From (1), we have:
3^(x-2y) = 3^(2x+2)
x-2y = 2x+2
x = -2y-2 .... (3)
From (2), we have:
5^(x-y) = 5^3
x-y = 3 ... (4)
Sub. (3) into (4).
-2y-2-y = 3
-3y-2 = 3
y = -5/3
Sub. y = -5/3 into (3).
x = -2(-5/3) - 2
x = 4/3
參考: myself
2012-05-20 4:31 am
3^(x-2y)=9^(x+1) i
5^(x-y)=125 ii
由i, 3^(x-2y)=3^(2)(x+1)
x-2y=2x+2
-2y=x+2
y=(x+2)/-2 iii
由ii, 5^(x-y)=5^3
x-y=3 iv
代iii入iv
x-(x+2)/2=3
2x-x+2=5
x=3
代x=3入iv
3-y=3
y=-1
所以
(x,y)=(3,-1)
5^(x-y)=125 ii
由i, 3^(x-2y)=3^(2)(x+1)
x-2y=2x+2
-2y=x+2
y=(x+2)/-2 iii
由ii, 5^(x-y)=5^3
x-y=3 iv
代iii入iv
x-(x+2)/2=3
2x-x+2=5
x=3
代x=3入iv
3-y=3
y=-1
所以
(x,y)=(3,-1)
收錄日期: 2021-05-02 14:13:40
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https://hk.answers.yahoo.com/question/index?qid=20120518000051KK00548