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The product of two numbers is 144, and their sum is 24. What are the two numbers?

Question

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Solution

To solve this problem, we can use the method of solving quadratic equations.

Step 1: Let's denote the two numbers as x and y. From the problem, we know that:

x*y = 144 (equation 1) x + y = 24 (equation 2)

Step 2: From equation 2, we can express y as y = 24 - x.

Step 3: Substitute y in equation 1 with 24 - x, we get:

x * (24 - x) = 144 24x - x^2 = 144 x^2 - 24x + 144 = 0

Step 4: This is a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -24, and c = 144. We can solve it using the quadratic formula x = [-b ± sqrt(b^2 - 4ac)] / (2a).

Step 5: Substitute a, b, and c into the formula, we get:

x = [24 ± sqrt((-24)^2 - 41144)] / (2*1) x = [24 ± sqrt(576 - 576)] / 2 x = [24 ± 0] / 2

Step 6: So the solutions are x = 24/2 = 12 and x = 24/2 = 12.

Step 7: Substitute x = 12 into equation 2, we get y = 24 - 12 = 12.

So the two numbers are 12 and 12.

This problem has been solved

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