Question

The product of two consecutive negative integers is 182

Answer 1

Answer:

The two numbers are -14, -13

Step-by-step explanation:

Let one number be -x

Since other number is consecutive then it should be  -x+1.

It is given that their product is 182.

then

-x*(-x+1) = 182

=> x^2 -x = 182

==> x^2 -x -182 = 0

solving for x

 $x^2 -x - 182 = 0\\=> x^2 + 14x - 13x - 182 = 0\\=>x(x+14) -13(x+14)\\=>(x+14) (x-13) = 0\\x+14 = 0 \ or \ x-13 = 0\\x = -14 \ or \ x = 13$

Given that the numbers are negative then 13 can not be value of x

Thus x = -14

other number = -x+1 = 14+1 = -13.

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