Question

find two consecutive positive even integers the sum of whose squares is 340

Answer 1

(12)^2+(14)^2→
144+196=340
Therefore the two no.s are 12 and 14.

Answer 2

Hey there !!!

let two consecutive even integers  be x and x+2

So according to question sum of their squares is 340.

        x²+(x+2)²=340

   x²+x²+4x+4=340

       2x²+4x+4-340=0

       2x²+4x-336=0

          x²+2x-168=0

         x²+14x-12x-168=0

     x(x+14)-12(x+14)=0

    (x+14)(x-12)=0

  x=-14 or x=12

But according to question numbers are positive even integers 

So x=12 and x+2=14

12,14 are numbers whose sum of squares is 340.

Verification:

12²+14²=144+196=340


Hope this helped you.....................