Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ A=7.\\ b.\ B=-1.\ \\ c.\ C=-5.\ \\ d.\ D=3.\\ e.\ E=-3.\ \\ f.\ F=20.\ \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ A=x+2.3\sqrt{x} +9-2=\left(\sqrt{x} +3\right)^{2} -2\geqslant 7\forall x\geqslant 0\\ Vậy\ GTNN\ A=7.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0\\ b.\ B=\left( 2\sqrt{x}\right)^{2} +2.3.2\sqrt{x} +9-10=\left( 2\sqrt{x} -3\right)^{2} -10\geqslant ( -3)^{2} -10=-1\\ Vậy\ GTNN\ B=-1.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0\\ c.\ C=\left( 3\sqrt{x}\right)^{2} +2.2.3\sqrt{x} +4-9=\left( 3\sqrt{x} +2\right)^{2} -9\geqslant 2^{2} -9=-5\\ Vậy\ GTNN\ C=-5.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0\\ d.\ D=\left( 5\sqrt{x}\right)^{2} +2.5\sqrt{x} +1+2=\left( 5\sqrt{x} +1\right)^{2} +2\geqslant 1+2=3\\ Vậy\ GTNN\ D=3.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0\\ e.\ E=\left( 4\sqrt{x}\right)^{2} +2.4\sqrt{x} +1-4=\left( 4\sqrt{x} +1\right)^{2} -4\geqslant 1-4=-3\\ Vậy\ GTNN\ E=-3.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0\\ f.\ F=x+2.12\sqrt{x} +144-124=\left(\sqrt{x} +12\right)^{2} -124\geqslant 12^{2} -124=20\\ Vậy\ GTNN\ F=20.\ Dấu\ "="\ xảy\ ra\ \Leftrightarrow x=0 \end{array}$
