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?

( n + 5)( n + 4) = 0
( n - 5)( n - 4) = 0
( n + 5)( n - 4) = 0
( n - 5)( n + 4) = 0

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

Hope this helps :)

Step-by-step explanation:

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step-by-step explanation: