高考问答暗黑3难度和悬赏掉落:初一数学
来源：百度文库 编辑：高考问答 时间：2024/04/28 17:02:33
若m,n是整数，且n^2+3m^2n^2=30m^2+517,则3m^2n^2的值为________
需要过程
需要过程
n^2+3m^2n^2=30m^2+517
n^2[1+3m^2]=10[3m^2+1]+507
[n^2-10][3m^2+1]=507=13*13*3
n^2-10=3*13=39
n=7
3m^2+1=13
m=2
3m^2n^2=3*2*2*7*7=588
已知n^2+3m^2n^2=30m^2+517
（3m^2+1）n^2=30m^2+517
（30m^2+517）/（3m^2+1）=n^2
30m^2+517=3m^2n^2+n^2
3m^2n^2=30m^2+517-n^2