m+n=3,mn=1,求2m^2+4n^2-6n+ - 知识问答

m+n=3,mn=1,求2m^2+4n^2-6n+2012的值.

1个回答

m+n=3,mn=1
(3-n)n=1
3n-n^2=1
n^2-3n+1=0
n^2-3n=-1
2m^2+4n^2-6n+2012
=2(m^2+n^2+2mn-2mn)+2n^2-6n+2012
=2(m+n)^2-4mn+2(n^2-3n)+2012
=2*3^2-4*1+2*(-1)+2012
=18-4-2+2012
=2024

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