Question

) The sum of squares of two consecutive
odd positive integers in 970. We need to
find those integers.​

Answer 1

Answer:

21 and 23

Explanation:

21*21=441

23*23=529

441+529=970

Answer 2

Answer:  Let the integers be x and (x+2)

             Therefore, x^2 + (x+2)^2 = 970

                               =) x^2 + x^2 + 4x + 4 = 970

                               =) 2x^2 + 4x + 4 = 970

                                =) 2x^2 + 4x = 970 - 4 = 966

                                =) 2x^2 + 4x - 966 = 0

                                 =) 2 ( x^2 + 2x  - 483) = 0

                                  =) x^2 + 2x - 483 = 0

                                   =) x^2 - 21x + 23x - 483 = 0

                                   =) x ( x-21) + 23 ( x - 21) = 0

                                   =) (x - 21) ( x + 23) = 0

      now, x - 21 =0                                 and, x + 23 + 0

               =) x = 21                                         =) x = -23 ( which is not possible)

    Hence, one integer is = x = 21

                   other integer is = x+2 = 21 + 2 =23

So, the two positive odd  integers are 21 and 23.

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