回復 6# jasonmv6124 的帖子
第11題
\(\begin{align}
& {{x}^{2}}+1+\sqrt{{{x}^{4}}-8x+8} \\
& =\sqrt{{{\left( {{x}^{2}}-1 \right)}^{2}}+{{\left( 2x-0 \right)}^{2}}}+\sqrt{{{\left( {{x}^{2}}-2 \right)}^{2}}+{{\left( 2x-2 \right)}^{2}}} \\
\end{align}\)
是拋物線\({{y}^{2}}=4x\)上一點\(P\left( {{x}^{2}},2x \right)\)到\(F\left( 1,0 \right)\)和\(A\left( 2,2 \right)\)距離和之最小值
易知\(P\left( 1,2 \right),\overline{PA}+\overline{PF}=3\)