Question

The sum of the square of two consecutive positive integer is 365 . find the Integers?​

Answer 1

Step-by-Step Explanation:

Let the two consecutive Numbers be x and x+1.

  Therefore ,

          x² + (x+1)² = 365

          x² + x² +1² + 2*x*1 = 365 (because (A+B)² = A² + B²+ 2AB)

      or 2x² + 1 + 2x = 365

        2x² + 2x = 365 - 1

        2x² + 2x = 364

        2(x² + x) = 364

      or x² + x = 364/2

      or x² + x = 182

    or x² + x - 182 =0

    Now Solve the Quadratic Equation ,

            x² + 14x - 13x - 182 = 0

Note : - 13 *14 = 182 , this is because I write 14x - 13x instead of x , so as to solve the quadratic equation .

         x (x+14) - 13 (x +14 ) = 0

         (x- 13) (x+14) = 0

         Therefore, Either x - 13 = 0 or x+14 =0

         Since the Consecutive Integers are positive,

         Therefore, x-13 = 0

                            ⇒ x =13

Hence One of the Positive Integers = 13.

Therefore other positive integer = x+1 = 13+1 = 14

So the two consecutive positive Integers are 13 and 14 .

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