Geomania.Org Forumları
Fantezi Cebir => Analiz-Cebir => Konuyu başlatan: yasarfaith - Temmuz 15, 2011, 10:01:53 ös
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kolay gelsin...
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(http://latex.codecogs.com/gif.latex?\hspace{-10}P(1)=827\Leftrightarrow%20P(1)-1\times827=0$\\\\%20$P(1)=1654\Leftrightarrow%20P(1)-2\times827=0$\\\\%20$P(1)=2481\Leftrightarrow%20P(1)-3\times827=0$\\\\%20So%20We%20can%20write%20as\\\\%20$P(x)-x\times%20827=0$,%20Where%20$x=1,2,3$%20are%20the%20roots%20of%20a%20Polynomial.\\\\%20but%20$P(x)$%20is%20a%20$4^{th}$%20degree%20polynomial.%20So%20It%20has%20$4$%20Roots.\\\\%20Let%20$x=\delta$%20be%20$4^{th}$%20of%20Given%20equation.\\\\%20$P(x)-x\times%20827=(x-1)(x-2)(x-3)(x-\delta)=0$\\\\%20$P(x)=(x-1)(x-2)(x-3)(x-\delta)+x\times%20827$\\\\%20Put%20$x=9,$\;We%20Get\\\\%20$P(9)=8\times7\times6\times(9-\delta)+9\times%20827$\\\\%20Similarly%20Put%20$x=-5,$\;%20We%20Get\\\\%20$P(-5)=6\times%207\times8\times(5+\delta)-5\times827$\\\\%20$P(9)+p(-5)=6\times7\times8\times14+4\times827$\\\\%20$\boxed{\boxed{\frac{P(9)+p(-5)}{4}=6\times7\times2\times14+827=2003}}$)
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thx...