2、证明:X(X+1)(X+2)(X+3)+1是完全平方
来源:百度知道 编辑:UC知道 时间:2024/05/19 22:42:19
另a=x2(平方)+3x
[(X+1)(X+2)]*[X(X+3)]+1
=(a+2)*a+1
=a2+2a+1
=(a+1)2(平方)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!另a=2X(平方)+3x
[(X+1)(X+2)]*[X(X+3)]+1
=(a+2)*a+1
=a*a+2a+1
=(a+1)2(平方)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!楼上的错了
证明:原式=X(X+3) (X+1)(X+2) +1
=(X2+3X)(X2+3X+2)+1
=(X2+3X)2+2(X2+3X)+1
=(X2+3X+1)2
所以原式是完全平方
[(X+1)(X+2)]*[X(X+3)]+1
=(a+2)*a+1
=a2+2a+1
=(a+1)2(平方)
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2、证明:X(X+1)(X+2)(X+3)+1是完全平方
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