若(x+2)(x+3)(x+4)(x+5)+k是完全平方公式,则k的值为多少?

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若(x+2)(x+3)(x+4)(x+5)+k是完全平方公式,则k的值为多少?
若(x+2)(x+3)(x+4)(x+5)+k是完全平方公式,则k的值为多少?

若(x+2)(x+3)(x+4)(x+5)+k是完全平方公式,则k的值为多少?
(x+2)(x+3)(x+4)(x+5)+k
=(x+3)(x+4)(x+2)(x+5)+k
=(x^2+7x+12)(x^2+7x+10)+k
=(t+12)(t+10)+k
=t^2+22t+120+k
=(t+11)^2+k-1
是完全平方式,所以k-1=0
k=1

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