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数学
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1991*1992*1993*1994+1-(1992*1992+1991)*(1992*1992+1991)
人气:201 ℃ 时间:2019-08-20 14:11:06
解答
令a=1992
则1991*1992*1993*1994+1-(1992*1992+1991)*(1992*1992+1991)
=(a-1)a(a+1)(a+2)-[a^2+(a-1)]^2
=[(a-1)(a+2)][a(a+1)]-(a^2+a-1)
=[(a^2+a)-2](a^2+a)-[(a^2+a)-1]^2
=(a^2+a)^2-2(a^2+a)-[(a^2+a)^2-2(a^2+a)+1]
=(a^2+a)^2-2(a^2+a)-(a^2+a)+2(a^2+a)-1
=-1
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