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The positive difference between the cubes of two positive consecutive integers is equal to 1801. Find these integers. Begin your solution by denoting them k and k + 1

 Jun 27, 2021
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( k+1)^3 - k ^3  = 1801

k^3  + 3k^2 +3k+1    - k^3 = 1801

3k^2 + 3k -1800 = 0

k^2 + k -600 = 0                   Qudratic formula shows k= 24   (the positive answer)     then k+1 = 25

 Jun 27, 2021

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