若m、n是整数,且n²+3m²n²=30m²+517,则3m²n
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若m、n是整数,且n²+3m²n²=30m²+517,则3m²n²的值为( )
n²+3m²n²=30m²+517
n^2+3m^2n^2-30m^2=517
n^2+3m^2(n^2-10)=517
n^2-10+3m^2(n^2-10)=517-10
(3m^2+1)(n^2-10)=507=3*13*13
n^2-10=39,3m^2+1=13
n^2=49,m^2=4
3m²n²=3*4*49=588
n^2+3m^2n^2-30m^2=517
n^2+3m^2(n^2-10)=517
n^2-10+3m^2(n^2-10)=517-10
(3m^2+1)(n^2-10)=507=3*13*13
n^2-10=39,3m^2+1=13
n^2=49,m^2=4
3m²n²=3*4*49=588
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