Câu hỏi của Trần Thị Hồng Ngọc

Question

Cho đa thức f(x)=x99-3000.x98+3000.x97 -3000.x96+....-3000.x2+3000.x-1

Bùi nguyễn quỳnh anh · Accepted Answer

ta có:3000=2009+1
\Rightarrow f(2009)=200999200999-3000.200998200998+3000.200997200997-3000.200996200996+...+3000.2009-1
=200999200999-(2009+1)200998200998+(2009+1).200997200997-(2009+1).200996200996+...+(2009+1).2009-1
=200999200999-(200999200999+200998200998)+(200998200998+200997200997)-(200997200997)+.200996200996)+...+(2009220092+2009)-1
=200999200999-200999200999-200998200998+200998200998+200997200997-200997200997-200996200996+...+2009220092+2009-1
=2009-1
=2008Câu trả lời: ta có:3000=2009+1
\Rightarrow f(2009)=200999200999-3000.200998200998+3000.200997200997-3000.200996200996+...+3000.2009-1
=200999200999-(2009+1)200998200998+(2009+1).200997200997-(2009+1).200996200996+...+(2009+1).2009-1
=200999200999-(200999200999+200998200998)+(200998200998+200997200997)-(200997200997)+.200996200996)+...+(2009220092+2009)-1
=200999200999-200999200999-200998200998+200998200998+200997200997-200997200997-200996200996+...+2009220092+2009-1
=2009-1
=2008

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