Discussion

The sum of two numbers is 25 and their product is 156. Find the smaller number.

Answer: A

Let the numbers be x and y. x + y = 25 and xy = 156.

We can form a quadratic equation: \(t^2 - (sum)t + (product) = 0\).

\(t^2 - 25t + 156 = 0\).

We need to find two numbers that multiply to 156 and add up to 25. These are 12 and 13.

\((t-12)(t-13) = 0\).

The numbers are 12 and 13. The smaller number is 12.

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