Question
The sum of two numbers is 30 whereas the sum of their
reciprocals is (5/12). Find the square of the product of the two numbers.Solution
Let the two numbers be x and y. Given: x + y = 30 1/x + 1/y = 5/12 Use: 1/x + 1/y = (x + y) / (xy) So: 30 / (xy) = 5 / 12 Cross-multiply: 30 * 12 = 5 * (xy) 360 = 5xy xy = 72 Square of the product: (xy)2 = 722 = 5184
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