Question 1130446
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A formal algebraic solution as shown by the other tutor is of course valid.  But if an algebraic solution is not required, solve the problem by logical reasoning and a bit of mental arithmetic, knowing that the numbers are even integers.<br>
Half the sum of the reciprocals is 9/80, which is about 1/9.  So try 8 and 10 as the two consecutive even integers.  They work; so they are the answers.<br>
And here is another way to solve the problem using logical reasoning.  The reciprocals of the two even integers, added together, yield a fraction with denominator 40.  So a more advanced student might also solve the problem by finding two consecutive even integers whose least common multiple is 40; the answer is again 8 and 10.