TN 10TH MATHS EM CH-2 EXAMPLE 2.3

 

Example  2.3

                Show that the square of an odd integer is of the form 4q+1, for some integer q.

 

Solution:

                Let x be any odd integer.

          An even integer x=2k let

                 Odd integer x=2k+1

GIVEN THAT

The square of an odd integer x² = (2k+1)²

                                                      = (2k)²+2(2k)(1)+ 1²

                                                      = 4k²+4k+1

                                                      = 4 k(k +1)+1

                                                  x² =4q+1   (where q= k(k +1) is        

                                                                            some integer)

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