a=2分之5-根号21,求a(a-1)(a-2)(a-3)(a-4)(a-5)的值
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a=2分之5-根号21,求a(a-1)(a-2)(a-3)(a-4)(a-5)的值
a=2分之5-根号21,求a(a-1)(a-2)(a-3)(a-4)(a-5)的值
a=2分之5-根号21,求a(a-1)(a-2)(a-3)(a-4)(a-5)的值
a(a-1)(a-2)(a-3)(a-4)(a-5)=(2分之5-根号21)(2分之3-根号21)(2分之1-根号21)
(-2分之5-根号21)(-2分之3-根号21)(-2分之1-根号21)
=-(2分之5-根号21)^2*(2分之3-根号21)^2*(2分之1-根号21)^2
也就是说a与(a-5)配对构成一个平方,(a-1)与(a-4)配对,(a-2)与(a-3)配对.这样一共有三个负平方,最后把每个平方算出来相乘就好了.会了么?
自己算最终值哈.
∵a=(5-√21)/2
∴2a-5=-√21
4a²-20a+25=21
a²-5a=-1
a(a-1)(a-2)(a-3)(a-4)(a-5)
=[a(a-5)][(a-1)(a-4)][(a-2)(a-3)]
=(a²-5...
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∵a=(5-√21)/2
∴2a-5=-√21
4a²-20a+25=21
a²-5a=-1
a(a-1)(a-2)(a-3)(a-4)(a-5)
=[a(a-5)][(a-1)(a-4)][(a-2)(a-3)]
=(a²-5a)(a²-5a+4)(a²-5a+6)
=(-1)×(-1+4)×(-1+6)
=-15
收起
a(a-1)(a-2)(a-3)(a-4)(a-5)
=a(a-5)*(a-1)(a-4)*(a-2)(a-3)
(利用公式(x+y)(x-y)=x^2-y^2)
=(21-25/4)+(21-9/4)+(21-1/4)
=237/4
=59.25