(x+2)^2004=(x+2)^2006
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Ta có : \(\frac{x^2-2008}{2007}+\frac{x^2-2007}{2006}+\frac{x^2-2006}{2005}=\frac{x^2-2005}{2004}+\frac{x^2-2004}{2003}+\frac{x^2-2003}{2002}\)
=> \(\frac{x^2-2008}{2007}+1+\frac{x^2-2007}{2006}+1+\frac{x^2-2006}{2005}+1=\frac{x^2-2005}{2004}+1+\frac{x^2-2004}{2003}+1+\frac{x^2-2003}{2002}+1\)
=> \(\frac{x^2-2008}{2007}+\frac{2007}{2007}+\frac{x^2-2007}{2006}+\frac{2006}{2006}+\frac{x^2-2006}{2005}+\frac{2005}{2005}=\frac{x^2-2005}{2004}+\frac{2004}{2004}+\frac{x^2-2004}{2003}+\frac{2003}{2003}+\frac{x^2-2003}{2002}+\frac{2002}{2002}\)
=> \(\frac{x^2-1}{2007}+\frac{x^2-1}{2006}+\frac{x^2-1}{2005}=\frac{x^2-1}{2004}+\frac{x^2-1}{2003}+\frac{x^2-1}{2002}\)
=> \(\frac{x^2-1}{2007}+\frac{x^2-1}{2006}+\frac{x^2-1}{2005}-\frac{x^2-1}{2004}-\frac{x^2-1}{2003}-\frac{x^2-1}{2002}=0\)
=> \(\left(x^2-1\right)\left(\frac{1}{2007}+\frac{1}{2006}+\frac{1}{2005}-\frac{1}{2004}-\frac{1}{2003}-\frac{1}{2002}\right)=0\)
=> \(x^2-1=0\)
=> \(x^2=1\)
=> \(x=\pm1\)
Vậy phương trình có 2 nghiệm là x = 1, x = -1 .
Cho f( x ) = x mũ 2005- 2006.x mũ 2004+ 2006.x mũ 2003-....- 2006.x mũ 2+ 2006.x mũ 1.
Tính f( 2005)
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x=2005
nên x+1=2006
\(f\left(x\right)=x^{2005}-x^{2004}\left(x+1\right)+x^3\left(x+1\right)-...+x\left(x+1\right)\)
\(=x^{2005}-x^{2005}-x^{2004}+x^{2004}+...-x^3-x^2+x^2+x\)
=x=2005
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Ta có :
\(x=2005\Rightarrow x+1=2006\)
Thay \(2006=x+1\) vào biểu thức trên ta được :
\(x^{2005}-\left(x+1\right)x^{2004}+\left(x+1\right)x^{2003}-\left(x+1\right)x^{2002}+...-\left(x+1\right)x^2+\left(x+1\right)x-1\)
\(=x^{2005}-x^{2005}+x^{2004}-x^{2004}+x^{2003}-...-x^3+x^2-x^2+x-1\)
\(=x-1\) mà \(x=2005\)
\(\Rightarrow x^{2005}-2006.x^{2004}+2006.x^{2003}-2006.x^{2002}+...-2006.x^2+2006x-1=2005-1=2004\)
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\(\frac{2-x}{2004}-1=\frac{1-x}{2005}-\frac{x}{2006}\)
\(\Leftrightarrow\frac{2-x}{2004}-1+2=\frac{1-x}{2005}+1-\frac{x}{2006}+1\)
\(\Leftrightarrow\frac{2006-x}{2004}=\frac{2006-x}{2005}-\frac{2006-x}{2006}\)
\(\Leftrightarrow\frac{2006-x}{2004}-\frac{2006-x}{2005}+\frac{2006-x}{2006}=0\)
\(\Leftrightarrow\left(2006-x\right)\left(\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2006}\right)=0\)
\(\Leftrightarrow2006-x=0\). Do \(\frac{1}{2004}-\frac{1}{2005}+\frac{1}{2006}\ne0\)
\(\Leftrightarrow x=2006\)
Cho biểu thức hai biến f(x,y) = \left(3x-5y+2\right)\left(2x+4y-4\right)f(x,y)=(3x−5y+2)(2x+4y−4).
Tìm các giá trị của yy sao cho phương trình (ẩn xx) f(x,y)=0f(x,y)=0 nhận x=2x=2 làm nghiệm.
Trả lời: y=y=
hoặc y=y=
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\(\frac{2006}{2008}\times\frac{2001}{2004}\times\frac{2008}{2002}\times\frac{2004}{2006}\times\frac{1001}{2001}=\frac{2006.2001.2008.2004.1001}{2008.2004.2002.2006.2001}\)
\(=\frac{\left(2001.2004.2006.2008.\right).1001}{\left(2001.2004.2006.2008\right).2002}=\frac{1001}{2002}=\frac{1001.1}{1001.2}=\frac{1}{2}\)
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