若xy是正整数,且 2的x次方 乘 4的y次方 =64,则x+y为

题目

若xy是正整数,且 2的x次方 乘 4的y次方 =64,则x+y为

答案

(2^x) * (4^y) = 64
2^x * 2^2y = 2^6
x+2y = 6
因为xy是正整数
1. x, y为负数 => x+2y < 0
2. x或y有一个为负数或0 => xy < 0 或 xy = 0
考虑 x+2y = 6
若y = 2 => x = 2 => x+y = 4
若y = 1 => x = 4 => x+y = 5

期待更好的解答
谢谢 ^_^