Your identity says ...
... sum of cubes = (sum)³ -3(product)(sum)
... = 4³ -3·1·4
... = 64 -12 = 52
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The two numbers are 2±√3, and the sum of their cubes is indeed 52.
Couldn't it be 54, 53 52, or 51
Since 1 lap I every 6 minutes then 30\6 is 5 so the answer is 5 LAPS
