What are two numbers that add up to equal 1 and multiply to equal -182

Question

2 numbers that add up to equal 1 and multiply to equal -182

Answer 1

Given 2 numbers that add to 1 and multiply to -182 we can set up two equations.

 

x + y = 1

(x)(y) = -182

 

we can solve for x in terms of y from the first equation and then substitute into the 2nd equation

 

x = 1-y

 

plug that into the 2nd equation we get

 

(1-y)(y) = -182

 

multiply this out giving

 

y - y^2 = -182

 

let's get a quadratic out of this by moving everything to one side giving

 

y^2 - y -182 = 0

 

We can factor this by finding the factors of -182 that add to -1 based on the coefficients in the equation

 

182 = (2)(7)(13) .... so we can see that 182 = 14(13) and (-14)(13) would give -182 and also add to -1

 

Thus the factoring of y - y^2 - 182 would give:

 

(y-14)(y+13) = 0

 

This can only be true if y is either 14 or -13

 

So the two numbers that add to 1 and multiply to -182 are 14, -13

 

Answer 2

Hi Adam--

 

Best thing to do is get the factor pairs of 182 (don't worry about the negative for now) until you find a pair whose difference is 1.

 

1 and 182
2 and 91

etc till you get two right next to one another.

 

then make the smaller one negative and ADD them to get 1.

 

{Stuck on factoring? Just divide 182 by each integer--whatever quotients are not whole numbers, chuck 'em--they don't matter.}

 

Hope this helps!

 

Matt in New York

 

ps: here's another hint: the smaller number is prime, the larger is a multiple of 7...