已知a=(5-根号21)/2,求代数式a(a-1)(a-2)(a-3)(a-4)(a-5)的值

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已知a=(5-根号21)/2,求代数式a(a-1)(a-2)(a-3)(a-4)(a-5)的值
已知a=(5-根号21)/2,求代数式a(a-1)(a-2)(a-3)(a-4)(a-5)的值

已知a=(5-根号21)/2,求代数式a(a-1)(a-2)(a-3)(a-4)(a-5)的值
∵a=(5-根号21)/2
∴2a-5=-√21
∴4a²-20a+25=21
∴a²-5a+1=0
∴a²-5a=-1
,a(a-1)(a-2)(a-3)(a-4)(a-5)
=a(a-5)(a-2)(a-3)(a-1)(a-4)
=(a²-5a)(a²-5a+6)(a²-5a+4)
=-1×(-1+6)×(-1+4)
=-15