The sum of the squares of 2 consecutive negative integers is 41. What are the numbers? Which of the following equations is the result of using the factoring method to solve the problem?
Accepted Solution
A:
Answer: The two numbers are -5 and -4
Explanation: Assume that the first number is x and that the second number is x+1. We know that the sum of their squares is 41. This means that: x² + (x+1)² = 41
We will expand the brackets and factorize to get the value of x as follows: x² + (x+1)² = 41 x² + x² + 2x + 1 = 41 2x² + 2x + 1 - 41 = 0 2x² + 2x - 40 = 0 We can divide all terms by 2 to simplify the equation: x² + x - 20 = 0 ..........> equation required in part II
Now, we can factorize this equation to get the values of x: x² + x - 20 = 0 (x-4)(x+5) = 0 either x = 4 .........> rejected because we know that x should be negative or x = -5 ...........> accepted
Based on the above calculations, the two numbers are -5 and -4