Question

The sum of two consecutive negative integers whose product is 156. Find the integers

Answer 1

The integers are -13 and -12

Explanation:

Let

x ----> the first consecutive negative integer

x+1 ----> the second consecutive negative integer

we know that

`x(x+1)=156`

Apply the distributive property

`x^2+x=156\\x^2+x-156=0`

The formula to solve a quadratic equation of the form

`ax^(2) +bx+c=0`

is equal to

`x=\frac{-b(+/-)\sqrt{b^(2)-4ac}} {2a}`

in this problem we have

`x^2+x-156=0`

so

`a=1\\b=1\\c=-156`

substitute in the formula

`x=\frac{-1(+/-)\sqrt{1^(2)-4(1)(-156)}} {2(1)}`

`x=\frac{-1(+/-)√(625)} {2}`

`x=\frac{-1(+/-)25} {2}`

`x_1=\frac{-1(+)25} {2}=12` ----> the solution cannot be a positive number

`x_1=\frac{-1(-)25} {2}=-13`

therefore

`x=-13\\x+1=-12`