Two consecutive even integers are such that the sum of their reciprocals is

MATHEMATICS · Multi-part · CBSE · Mathematics · Algebra Play · Algebra Play

Problem

\dfrac{5}{12}

. Attempt the following tasks: (i) If the smaller even integer is

2n

, express the next consecutive even integer in terms of

n

and obtain an equation using the given condition on their reciprocals. (ii) Transform the relation of part (i) into a quadratic equation in

n

and solve it. (iii) Write the two even integers and verify that the sum of their reciprocals is indeed

\dfrac{5}{12}

. (iv) Calculate the difference between the two integers found in part (iii).