若m、n是整数,且n²+3m²n²=30m²+517,则3m²n²的值为（ ）
问题描述：
若m、n是整数,且n²+3m²n²=30m²+517,则3m²n²的值为（ ）
答
n²+3m²n²=30m²+517n^2+3m^2n^2-30m^2=517n^2+3m^2(n^2-10)=517n^2-10+3m^2(n^2-10)=517-10(3m^2+1)(n^2-10)=507=3*13*13n^2-10=39,3m^2+1=13n^2=49,m^2=43m²n²=3*4*49=588