Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 1.\ \ A=-\frac{5}{4}\\ 2.\ \ B=\frac{3}{4}\\ 3.\ \ C=-2010\\ 4.\ \ D=-\frac{16061}{8}\\ 5.\ \ E=0\\ 6.\ \ F=-\frac{5}{4} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} 1.\ A=\left(\sqrt{x} +\frac{1}{2}\right)^{2} -\frac{5}{4} \geqslant -\frac{5}{4} \Rightarrow A\geqslant -\frac{5}{4}\\ GTNN\ của\ A=-\frac{5}{4}\\ 2.\ B=\left(\sqrt{x} -\frac{1}{2}\right)^{2} +\frac{3}{4} \geqslant \frac{3}{4} \Rightarrow B\geqslant \frac{3}{4}\\ GTNN\ của\ B=\frac{3}{4}\\ 3.\ C=\frac{1}{2}( 2x-1) +\sqrt{2x-1} -\frac{4019}{2} =\frac{1}{2}\left(\sqrt{2x-1} +1\right)^{2} -2010\geqslant -2010\\ \Rightarrow C\geqslant -2010\\ GTNN\ của\ C=-2010\\ 4.\ D=2( x-1) -\sqrt{x-1} -2008=2\left(\sqrt{x-1} -\frac{1}{4}\right)^{2} -\frac{16061}{8} \geqslant -\frac{16061}{8}\\ \Rightarrow D\geqslant -\frac{16061}{8}\\ GTNN\ của\ D=-\frac{16061}{8}\\ 5.\ E=\frac{1}{2}\left( 1-\frac{x}{2}\right) +\sqrt{1-\frac{x}{2}} +\frac{1}{2} =\frac{1}{2}\left(\sqrt{1-\frac{x}{2}} +1\right)^{2} \geqslant 0\\ \Rightarrow E\geqslant 0\\ GTNN\ của\ E=0\\ 6.\ F=2-x-\sqrt{2-x} -1=\left(\sqrt{2-x} -\frac{1}{2}\right)^{2} -\frac{5}{4} \geqslant -\frac{5}{4}\\ GTNN\ của\ F=-\frac{5}{4}\\ \end{array}$
