Question
The product of two positive
integers is 121 times the product of one integer and the reciprocal of the other. If the sum of these two integers is 28, find the square of the larger integer.Solution
ATQ, Let the two integers be ‘x’ and ‘y’ where x > y. Then, according to the question, x × y = x × (1/y) × 121 Or, xy = (121x/y) Or, 121x = xy2 So, y = √121 = 11 {since, ‘x’ and ‘y’ are positive integers} So, x = 28 – 11 = 17 Therefore, x2 = 172 = 289
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