若a的x次方=b的y次方=2001的z次方,(a,b为正整数)且x分之一+y分之一=z分之一,求a＋b的值
问题描述：
若a的x次方=b的y次方=2001的z次方,(a,b为正整数)且x分之一+y分之一=z分之一,求a＋b的值
答
a^x = b^y = 2001^z
xloga = ylogb = zlog2001
1/x = loga/(zlog2001)
1/y = logb/(zlog2001)
1/x + 1/y = logab /(zlog2001) = 1/z
log ab = log2001
ab = 2001
2001 = 3*667
a+b = 3+ 667 = 670
答
a^x = b^y = 2001^zxloga = ylogb = zlog20011/x = loga/(zlog2001) 1/y = logb/(zlog2001)1/x + 1/y = logab /(zlog2001) = 1/zlog ab = log2001ab = 20012001 = 3*667a+b = 3+ 667 = 670