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

There are two factors of -36 such that one factor is 11 less than half of the other factor. Choose all the pairs of these factors.

-2 and 18

-6 and 6

3 and -12

4 and -9

Guest Jan 18, 2019

#1**+1 **

First one....we have that

n^2 + ( n + 1)^2 = 41

n^2 + n^2 + 2n + 1 = 41

2n^2 + 2n - 40 = 0

n^2 + n - 20 = 0

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

Second one

Call the first factor, F

So...the second is F/2 - 11

So.....this implies that

(F) [ (F/2) - 11] = -36 simplify

F^2/2 - 11F = - 36

F^2/2 - 11F + 36 = 0 multiply through by 2

F^2 - 22F + 72 = 0

(F - 18) ( F - 4) = 0

F = 18 or F = 4

When F = 18 the other factor is : F/2 - 11 = 18/2 - 11 = 9 - 11 = -2

When F = 4 the other factor is 4/2 - 11 = 2 - 11 = -9

So....the factors are

(18, -2) and ( 4, - 9)

CPhill Jan 18, 2019

#2**0 **

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

(n - 5)(n - 4) = 0, This comes from this quadratic: n^2 - 9 n + 20 = 0

(n - 5)(n + 4) = 0, This comes from this quadratic: n^2 - n - 20 = 0

(n + 5)(n - 4) = 0, This comes from this quadratic: n^2 + n - 20 = 0

(n + 5)(n + 4) =0, This comes from this quadratic: n^2 + 9 n + 20 = 0

Guest Jan 18, 2019