Chứng minh rằng: $\frac{1}{3}\leq \frac{x^{2}+x+1}{x^{2}-x+1}\leq 3$
$\frac{1}{3}\leq \frac{x^{2}+x+1}{x^{2}-x+1}\leq 3$
Started By sherry Ai, 08-02-2012 - 12:40
#2
Posted 08-02-2012 - 15:17
Poseidont
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Dark Knight
ta có
$2(x-1)^{2}\geq 0\Rightarrow 2x^{2}-4x+2\geq 0\Rightarrow 3x^{2}-3x+3\geq x^{2}+x+1\Rightarrow P\leq 3$
$2(x+1)^{2}\geq 0\Rightarrow ...\Rightarrow P\geq \frac{1}{3}$
dpcm
$2(x-1)^{2}\geq 0\Rightarrow 2x^{2}-4x+2\geq 0\Rightarrow 3x^{2}-3x+3\geq x^{2}+x+1\Rightarrow P\leq 3$
$2(x+1)^{2}\geq 0\Rightarrow ...\Rightarrow P\geq \frac{1}{3}$
dpcm
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