cho f(x)=x8-101×7+101×6-101×5+……..+101×2-101x+25. tinh f(100) 08/08/2021 Bởi Kennedy cho f(x)=x8-101×7+101×6-101×5+……..+101×2-101x+25. tinh f(100)
Đáp án: `f(100)=-75` Giải thích các bước giải: Từ `x=100 to x+1=101` Ta có : `f(x)=x^8-101x^7+101x^6-101x^5+…+101x^2-101x+25` `=x^8-(x+1)x^7+(x+1)x^6-(x+1)x^5+….+(x+1)x^2-(x+1)x+25` `=x^8-x^8-x^7+x^7+x^6-x^6-x^5+….+x^3+x^2-x^2-x+25` `=-x+25=-100+25=-75` Vậy `f(100)=-75` Bình luận
Tính `f(100) => x= 100 => x – 100 =0` Ta có: `f(x) = x^8 – 101x^7 + 101x^6 – 101x^5 +…+ 101x^2 – 101x + 25` `f(x) = x^8 – (100+1)x^7 + (100+1)x^6 – (100+1)x^5 +…+(100+1)x^2 – (100+1)x + 25` `f(x) = x^8 – 100x^7 – x^7 + 100x^6 + x^6 – 100x^5 – x^5 +…+100x^2 + x^2 – 100x – x + 25` `f(x) = x^7(x – 100) – x^7(x – 100) + x^5(x – 100) +….+x(x – 100) – x+ 25` `f(x) = x^7 . 0 – x^7. 0 + …+ x . 0 – x + 25` `f(100) = -100 + 25` `f(100) = -75` Vậy `f(100) = -75` Bình luận
Đáp án:
`f(100)=-75`
Giải thích các bước giải:
Từ `x=100 to x+1=101`
Ta có : `f(x)=x^8-101x^7+101x^6-101x^5+…+101x^2-101x+25`
`=x^8-(x+1)x^7+(x+1)x^6-(x+1)x^5+….+(x+1)x^2-(x+1)x+25`
`=x^8-x^8-x^7+x^7+x^6-x^6-x^5+….+x^3+x^2-x^2-x+25`
`=-x+25=-100+25=-75`
Vậy `f(100)=-75`
Tính `f(100) => x= 100 => x – 100 =0`
Ta có: `f(x) = x^8 – 101x^7 + 101x^6 – 101x^5 +…+ 101x^2 – 101x + 25`
`f(x) = x^8 – (100+1)x^7 + (100+1)x^6 – (100+1)x^5 +…+(100+1)x^2 – (100+1)x + 25`
`f(x) = x^8 – 100x^7 – x^7 + 100x^6 + x^6 – 100x^5 – x^5 +…+100x^2 + x^2 – 100x – x + 25`
`f(x) = x^7(x – 100) – x^7(x – 100) + x^5(x – 100) +….+x(x – 100) – x+ 25`
`f(x) = x^7 . 0 – x^7. 0 + …+ x . 0 – x + 25`
`f(100) = -100 + 25`
`f(100) = -75`
Vậy `f(100) = -75`