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Use euclid's division lemma to show that the cube of any positive integer is of the form 9m, 9m+1 or9m+ 8

Posted by Manveer Singh 7 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Nipun Goyal 7 years, 7 months ago

0<r<3 So r can be =0,1,2 Case 1: (3m)cube=27m cube 9(3m cube) It is in the form 9m. Case 2: (3m +1)cube =(3m) cube +1+3(3m)(3m+1) =27m cube +1+27m square +9m =9(3m cube +3m square +m) +1 It is in the form 9m+1. Case 3: (3m+2)cube =(3m) cube +(2)cube +3(3m)(2) (3m+2) =27m cube +8+54m square +36m =9(3m cube+6m square +4m)+8 It is in the form 9m+8. So, the cube of any positive integer is of the form 9m,9m+1,9m+8.

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CBSE > Class 10 > Mathematics