Tìm GTNN của biểu thức

J

jet_nguyen

Ta có:
$$A= \dfrac{x^2 - 2x +2011}{x^2}$$$$\Longrightarrow Ax^2 = x^2 -2x + 2011 \, \ ( x\ne 0)$$$$\Longrightarrow (A-1)x^2 +2x-2011 = 0$$$$\Longrightarrow \Delta' = 1+2011(A-1)\ge 0 $$$$\Longrightarrow 2011A\ge 2010$$$$\Longrightarrow Min = \dfrac{2010}{2011}$$
 
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