Question 851631
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Hi,
two consecutive even integers:  x and (x+2)
Question States***
{{{1/x + 1/(x+2) = 21/220}}}
  {{{(2x+2)/x(x+2) = 21/220}}}    | Cross Multiplying 
   220(2x+2) = 21(x^2 + 2x)
   x^2 - 398x - 440 = 0 
{{{x = (398 +- sqrt( 195364))/(42) }}}
 {{{x = (398 +- sqrt( 442))/(42) }}}   (Tossing out the negative solution for unit measure)
   x = 20, two consecutive even integers are; 20, 22
CHECKING our answer***
{{{1/20 + 1/22 = 42/440 = 21/220}}}
Wish You the Best in your Studies.