ĐKXĐ: a $\neq$ 0
M = $\frac{a²-2a+2011}{a²}$
= $\frac{2011.(a²-2a+2011)}{2011a²}$
= $\frac{2010a²+a²-2.2011a+2011² }{2011a²}$
= $\frac{2010a²}{2011a²}$ + $\frac{a²-2.2011a+2011²}{2011a²}$
= $\frac{2010}{2011}$ + $\frac{(a-2011)²}{2011a²}$ ≥ $\frac{2010}{2011}$
( Vì $\frac{(a-2011)²}{2011a²}$ ≥ 0)
Dấu "=" xảy ra khi $\frac{(a-2011)²}{2011a²}$ = 0
<=> (a - 2011)² = 0
<=> a - 2011 = 0
<=> a = 2011 ( TM)
Vậy GTNN của M là $\frac{2010}{2011}$ khi a = 2011
