“数学之美”团员448755083为你解答!
2008*2009*2010*2012*2013*2014+36
=(2011-3)(2011-2)(2011-1)(2011+1)(2011+2)(2011+3)+36
=(2011²-1)(2011²-4)(2011²-9)+36
=(t-1)(t-4)(t-9)+36
=t³-14t²+49t
=t(t-7)²
∵t和(t-7)²都是完全平方数
∴原数字就是完全平方数.
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