(10點)>>>急<<< 數學問題-指數運算
2011-02-06 9:39 pm
回答 (5)
2011-02-06 10:11 pm
2011-02-07 1:08 am
6^X-4x3^X+3x2^X-12=0
故令2^X=Y且令3^X=Z
則得到
6^X-4x3^X+3x2^X-12=YZ-4Z+3Y-12
=Z(Y-4)+3(Y-4)=(Y-4)(Z+3)=0
故得到Y=4;Z=-3
故X=2
故令2^X=Y且令3^X=Z
則得到
6^X-4x3^X+3x2^X-12=YZ-4Z+3Y-12
=Z(Y-4)+3(Y-4)=(Y-4)(Z+3)=0
故得到Y=4;Z=-3
故X=2
2011-02-07 12:09 am
sol
6^x-4*3^x+3*2^x-12=0let 2^x=a
&3^x=b
6^x-4*3^x+3*2^x-12=ab-4b+3a-12
=b(a-4)+3(a-4)
=(b+3)(a-4)=0
if b=-4
a-4=0
a=4
2^x=a
x=2
x is only answer
2011-02-06 10:19 pm
2011-02-06 10:01 pm
參考: 上帝賜的聰明智慧
收錄日期: 2021-04-23 19:23:38
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20110206000015KK02947