(3√x^2乘√x^3)^n=x^m
2012-06-06 2:51 am
(3√x^2乘√x^3)^n=x^m where x＞0 ,m and n are positive integers, find the minimum value of n.
回答 (3)
2012-06-06 9:49 am
✔ 最佳答案
(3√x^2乘√x^3)^n=x^m[(x^2)^(1/3) 乘(x^3)^(1/2)]^n = x^m
[x^(2/3) 乘 x^(3/2)]^n = x^m
[(x^(2/3+3/2)]^n = x^m
[(x^(4/6+9/6)]^n = x^m
[(x^(13/6)]^n = x^m
(x^(13n/6) = x^m
13n/6 = m
n = 6m/13
n = (6/13)m
The minimum value of n (positive integer) so that m is a positive integer:
n = 6 and m = 13
The minimum value of n = 6 (Answer)
2012-06-06 3:43 am
√x^2 ??!!
2012-06-06 3:41 am
nlog9x+√x^3 = mlogx
(log 9x + √x^3)/logx=m/n
(9x+√x^3)/x = m/n
x(9+√1^3) /x = m/n
10 = m/n
(log 9x + √x^3)/logx=m/n
(9x+√x^3)/x = m/n
x(9+√1^3) /x = m/n
10 = m/n
收錄日期: 2021-04-13 18:43:37
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20120605000051KK00421