$證明:(2)x^{2}-12x+37=(x-6)^{2}+1,∵(x-6)^{2}≥0,∴(x-6)^{2}+1>0$
$∴無論x取何值,代數(shù)式x^{2}-12x+37的值是正數(shù)$
$(2)解:M-N=(2x^{2}+4x+5+y^{2})-(x^{2}+6x+4)=x^{2}-2x+1+y^{2}=(x-1)^{2}+y^{2}$
$∵(x-1)^{2}≥0,y^{2}≥0,∴(x-1)^{2}+y^{2}≥0,∴M≥N$
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