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Let L equal the larger of the two integers and S the smaller. Then L=2S.

Also L-1/S=1/S. Starting with this second equation and solving for L results in L=2/S. Equating the two values of L produces 2/S=2S and 1/S=S. The solutions to this last equation are S=1 or S=-1.

If L is to be the larger of the two integers, then S must equal 1 and L must equal 2.

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Q: The larger of two integer is twice the smaller when the recipical of the smaller integer is subtracted from the larger the result is the recipical of the smaller integer?
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