Explanation Given data: The product of two consecutive integers is 380. Method/Formula used: Two successive integers or the integers whose difference is 1 are known as consecutive integers.If x and y aretwo consecutive positive integers such that y is larger integer, then y − x = 1 . Calculation: Let x and y be two integers such that y > x (x is smaller number) then y − x = 1 ......(1) From the given information, the product of two given integers is 380, i.e., x × y = 380 ......(2) From equation (1), y = 1 + x . Substituting value of y in equation (2), x × ( 1 + x ) = 380 ⇒ x + x 2 = 380 ⇒ x + x 2 − 380 = 0 . Rearranging the terms, x 2 + x − 380 = 0 ......(3) Equation (3) is a quadratic equation that gives two values of x. This equation can be solved by split or factorisation method. For which first write factors of 380 and then by guess work find two number whose product is 380 and their sum or difference is 1. 380 = 2 × 2 × 5 × 19 , from the guess work one number is 2 × 2 × 5 = 20 and other number is 19

17th Edition

ISBN: 9780134650111

Author: Martin-Gay

Publisher: PEARSON

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Chapter 13, Problem 63R

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Chapter 13, Problem 62R

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Two consecutive positive integers whose product is given.

Solution Summary: The author explains that the product of two consecutive integers is 380, which can be solved by split or factorisation method.

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To find: Two consecutive positive integers whose product is given.

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