Chọn C
Ta có
\(\begin{array}{l} {\left|z+2w\right|^{2} +2\left|z-{\rm w}\right|^{2} } \\ {=(z+2w)(\overline{z}+2\overline{{\rm w}})+2(z-{\rm w})(\overline{z}-\overline{{\rm w}})} \\ {=3\left|z\right|^{2} +6\left|{\rm w}\right|^{2} \, \, \Rightarrow \, 8^{2} +6^{2} +2.4^{2} =\, 3\left|z\right|^{2} +6\left|{\rm w}\right|^{2} } \\ {\Rightarrow \, \left|z\right|^{2} +2\left|{\rm w}\right|^{2} =44\, \, \, \, \, (1)} \\ {} \end{array}\)
Từ \((1)\) và bất đẳng thức Cauchy --Schwaz ta có :
\(\begin{array}{l} {(\left|z\right|+\left|{\rm w}\right|)^{2} =(1.\left|z\right|+\frac{1}{\sqrt{2} } \sqrt{2} \left|{\rm w}\right|)^{2} \le (1^{2} +\frac{1}{2} )(\left|z\right|^{2} +2\left|{\rm w}\right|^{2} )} \\ {\Rightarrow \, \left|z\right|+\left|{\rm w}\right|\le \, \sqrt{66} } \end{array} \)
Suy ra đáp án C