Answers

2014-05-26T14:42:31+05:30
Any integer can be written in the form 5m , 5m+1, 5m+2 (where m is any integer)

(5m)² = 25m² = 5 X 5m² = 5q (where q = 5m²)

(5m+1)² = (5m)² + 2X 5m X 1 + 1² (by using identity- (a+b)²= a²+ 2ab +b² )
            = 25m² + 10 m + 1
            = 5 (5m²+ 2m) +1
            = 5q +1 ( q= 5m²+2m)
(5m+2)²= (5m)² + 2X 5m X 2 +2² (by using identity- (a+b)²= a²+ 2ab +b² )
           = 25m² + 20 m +4
           = 5 (5m²+4m ) + 4
           = 5q+4 (where q= 5m²+4m)
Hence proved :) :D


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