Give me an example with an explanation of how to solve the sum and product.
Answer (1)
Answer:To solve a sum and product problem, we typically look for two numbers that add up to a specific sum and multiply to a specific product.**Example:**Find two numbers that add up to 10 and multiply to 21.**Step 1: Set up the equations.**Let the two numbers be \( x \) and \( y \).We know:1. \( x + y = 10 \) (sum)2. \( xy = 21 \) (product)**Step 2: Express one variable in terms of the other.**From the sum equation, we can express \( y \) as:\[ y = 10 - x \]**Step 3: Substitute into the product equation.**Substituting into the product equation gives:\[ x(10 - x) = 21 \]\[ 10x - x^2 = 21 \]Rearranging it:\[ x^2 - 10x + 21 = 0 \]**Step 4: Solve the quadratic equation.**Now, we can factor or use the quadratic formula. Factoring:\[ (x - 3)(x - 7) = 0 \]Thus, \( x = 3 \) or \( x = 7 \).**Step 5: Find the corresponding \( y \) values.**If \( x = 3 \), then \( y = 10 - 3 = 7 \).If \( x = 7 \), then \( y = 10 - 7 = 3 \).**Conclusion:**The two numbers are 3 and 7. They satisfy both the sum (3 + 7 = 10) and product (3 * 7 = 21) requirements
