若m、n是整数,且n^2+3m^2n^2=30m^2+517,求3m^2n^2的值.
问题描述：
若m、n是整数,且n^2+3m^2n^2=30m^2+517,求3m^2n^2的值.
答
(3m^2+1)(n^2-10)=507=3*13*13
得3m^2+1=13,n^2-10=3*13
m^2=4,n^2=49
3m^2n^2=3*4*49=588
答
由n^2+3m^2n^2=30m^2+517得
(3m^2+1)(n^2-10)=507=3*13*13
因为m,n都是整数所以3m^2+1,n^2-10都是整数
容易得3m^2+1=13,n^2-10=3*13----------保证m,n是整数
故m^2=4,n^2=49
因此3m^2n^2=3*4*49=588