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[duonghieu]

Giải phương trình:
$(x+2009)^{2009}+(x+2009)^{2008}(x+2010)+...+(x+2009)(x+2010)^{2008}+(x+2010)^{2009}=0$

[donghaidhtt]

Giải phương trình:
$(x+2009)^{2009}+(x+2009)^{2008}(x+2010)+...+(x+2009)(x+2010)^{2008}+(x+2010)^{2009}=0$

$(x+2009)^{2009}+(x+2009)^{2008}(x+2010)+...+(x+2009)(x+2010)^{2008}+(x+2010)^{2009}=0$
$\Leftrightarrow \begin{bmatrix} (x+2010)-(x+2009) \end{bmatrix}. ((x+2009)^{2009}+(x+2009)^{2008}(x+2010)+...+(x+2009)(x+2010)^{2008}+(x+2010)^{2009})=0$
$\Leftrightarrow (x+2010)^{2010}-(x+2009)^{2010}=0$
$\Leftrightarrow \left | x+2010 \right |=\left | x+2009 \right |$
$\Leftrightarrow \left\{\begin{matrix} x+2010=x+2009\\ x+2010=-x-2009 \end{matrix}\right.$
$\Leftrightarrow x=\frac{-4019}{2}$
Vậy $x=\frac{-4019}{2}$

Edited by donghaidhtt, 26-11-2012 - 21:02.