Find $ mn $ using:
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- Question: A digital storytelling analyst creates a health app where interactive sequences are modeled by variables $ m $ and $ n $. If $ m + n = 10 $ and $ m^2 + n^2 = 58 $, determine $ m^3 + n^3 $.
- Solution: Given $ m + n = 10 $, $ m^2 + n^2 = 58 $.
- First, compute $ (m + n)^3 = 10^3 = 1000 $.
- \Rightarrow 100 = 58 + 2mn \Rightarrow 2mn = 42 \Rightarrow mn = 21
- Now substitute:
- m^3 + n^3 = 1000 - 3(21)(10) = 1000 - 630 = 370
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