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Lesson: 10.3 Applications: Quadratic Equat...
Question 3 of 4, Step 1 of 1

Find two positive numbers whose difference is 7 and whose product is 744 .

Answer
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Step 1 ：Let's denote the two positive numbers as x and y.

Step 2 ：From the problem, we know that the difference between these two numbers is 7, so we can write the equation \(x - y = 7\).

Step 3 ：We also know that the product of these two numbers is 744, so we can write the equation \(x * y = 744\).

Step 4 ：We can solve these two equations simultaneously to find the values of x and y.

Step 5 ：The solution contains two pairs of numbers, (-24, -31) and (31, 24). However, the problem asks for positive numbers, so we discard the pair (-24, -31) and take (31, 24) as the solution.

Step 6 ：Final Answer: The two positive numbers are \(\boxed{31}\) and \(\boxed{24}\).