m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)_数学解答

m,n是整数,n^2+3(m^2)(n^2)=30(m^2)+517,求3(m^2)(n^2)

人气：228 ℃　时间：2020-04-15 02:16:29

解答

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...