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?

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 :)

Hello!

the answer is:

the answer is:

why?

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!

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