Tính B= (x^2007+3.x^2006-1)^2007 tại x=-3
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Ta co
A=2007^2006( lên lơp 6 e se hoc)
=>A=2007^2 x 2007^2004
=>(...9)x(...1)=(...9) (1)
Ta co:
B=2006^2007=(...6)
B=\(\left(x^{2007}+3x^{2006}-1\right)^{2007}\)
\(B=\left[\left(-3^{2007}\right)+3\left(-3^{2006}\right)-1\right]^{2007}\)
\(B=\left[\left(-3^{2007}\right)+3.3^{2006}-1\right]^{2007}\)
\(B=\left[\left(-3^{2007}\right)+3^{2007}-1\right]^{2007}\)
\(B=\left(-1\right)^{2007}=\left(-1\right)\)
Ta có: \(B=\left(x^{2007}+3x^{2006}-1\right)^{2007}\)
Thay x = -3 vào B ta có:
\(B=\left(\left(-3\right)^{2007}+3\left(-3\right)^{2006}-1\right)^{2007}\)
=>\(B=\left(\left(-3\right)^{2007}+3\cdot3^{2006}-1\right)^{2007}\)
=>\(B=\left(\left(-3\right)^{2007}+3^{2007}-1\right)^{2007}\)
=>\(B=\left(0-1\right)^{2007}\)
\(=>B=\left(-1\right)^{2007}=-1\)
Ta có:B=\(\left(x^{2007}+3x^{2006}-1\right)^{2007}\)
\(\Rightarrow\)B=\(\left(\left(-3\right)^{2007}+3\times\left(-3\right)^{2006}-1\right)^{2007}\)
B=\(\left(\left(-3\right)\times\left(-3\right)^{2006}+3\times\left(-3\right)^{2006}-1\right)^{2007}\)
B=\(\left(\left(\left(-3\right)+3\right)\times\left(-3\right)^{2006}-1\right)^{2007}\)
B=\(\left(0\times\left(-3\right)^{2006}-1\right)^{2007}\)
B=\(\left(0-1\right)^{2007}\)
B=\(\left(-1\right)^{2007}\)
B=\(\left(-1\right)\)
Tại \(x=-3\) thì:
\(B=\left[-3^{2007}+3.\left(-3\right)^{2006}-1\right]^{2007}\)
\(\Rightarrow B=\left[-3^{2006}\left(-1+3\right)-1\right]^{2007}\)
\(\Rightarrow B=\left[-3^{2006}.2-1\right]^{2007}\)
\(x-\frac{x}{2}+\frac{x}{2}-\frac{x}{3}+...+\frac{x}{2006}-\frac{x}{2007}=\frac{2006}{2007}\)
\(x-\frac{x}{2007}=\frac{2006}{2007}\)
\(\frac{2007x-x}{2007}=\frac{2006}{2007}\)
\(\frac{2006x}{2007}=\frac{2006}{2007}\Rightarrow2006x=2006\)
=>x=1
a)=1/2*2/3......*19/20
=1/20
b)=3/2*4/3......*2008/2007
=3/2007
Tại x= - 3
=> \(B=\left[\left(-3\right)^{2017}+3\left(-3\right)^{2016}-1\right]^{2017}\)
=> \(B=\left[\left(-3\right)^{2017}+3^{2017}-1\right]^{2017}\)
=> \(B=\left(-1\right)^{2017}\)
=> B = - 1
Ta có:
\(B=\left(x^{2007}+3x^{2006}-1\right)^{2007}\)
\(B=\left(\left(-3\right)^{2007}+3\left(-3\right)^{2006}-1\right)^{2007}\)
\(B=\left(\left(-3\right)^{2007}+3\left(3\right)^{2006}-1\right)^{2007}\)
\(B=\left(\left(-3\right)^{2007}+3^1\left(3\right)^{2006}-1\right)^{2007}\)
\(B=\left(\left(-3\right)^{2007}+3^{1+2006}-1\right)^{2007}\)
\(B=\left(\left(-3\right)^{2007}+3^{2007}-1\right)^{2007}\)
\(B=\left(0-1\right)^{2007}\)
\(B=\left(-1\right)^{2007}\)
\(B=1\)
Ta có : B= (x^2007+3.x^2006-1)^2007
Thay x=-3 vào biểu thức B ta được:
B= [(-3)2007+3.(-3)2006 -1]2007
\(\Leftrightarrow\) [(-3)2006 .(-3)+3.(-3)2006 -1]2007
\(\Rightarrow\)[ (-3)2006 .(-3+3) -1]2007
\(\Rightarrow\) [(-3)2006 . 0-1]2007
\(\Rightarrow\) (0-1)2007
\(\Rightarrow\) (-1)2007 =-1
Vậy giá trị của biểu thức B= (x^2007+3.x^2006-1)^2007 tại x=-3 là -1(đpcm)
Chúc bạn học tốt!!!
\(B=\left(x^{2007}+3x^{2006}-1\right)^{2007}\)
\(\Rightarrow B=\left[\left(-3\right)^{2007}+3\left(-3\right)^{2006}-1\right]^{2007}\)
\(\Rightarrow B=\left[\left(-3\right)^{2006}.\left(-3+3\right)-1\right]^{2007}\)
\(\Rightarrow B=\left[\left(-3\right)^{2006}.0-1\right]^{2007}\)
\(\Rightarrow B=\left(-1\right)^{2007}\)
\(\Rightarrow B=-1\)
Vậy B = -1