Part 9

Algebra Level 3

m=3+2232213n=17+122+17122+23 \begin{aligned} m&=&\sqrt[3]{\sqrt{3+2\sqrt{2}}-\sqrt{3-2\sqrt{2}}-1} \\ n&=&\sqrt[3]{\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}+2} \end{aligned}

Let the values of mm and nn be described above. Compute 2(20m+6n)2322(20m+6n)^{2}-32.

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