The product of two consecutive integers is 182. Find the integers?

Question

The product of two consecutive integers is 272. Find the integers

Answer 1

272= 16*17

182= 13*14

Answer 2

by trial and improvement i found the integers were 16 and 17.

Answer 3

13 and 14 for 182.

16 and 17 for 272.

Answer 4

frist!

Answer 5

13 and 14, and do your own homework!

Answer 6

OK

Here is how to show how to do this:

(a)(a+1) = 182

a^2 + a = 182

a^2 + a - 182 = 0

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

So you have two possible solutions (if you include negative numbers)

-13 * -14 and 13 * 14

Hope that helps.

For 272 do the same thing:

a^2 + a - 272 = 0

(a +17)(a-16)= 0

16, 17 or -16, -17.

Hope that helps.

Answer 7

I think the easiest way to do this is take the square root and that will get you midway between the 2 integers. Try it.

Answer 8

x(x+1)=182

x^2+x-182=0

x=13

x+1=14

similarly

x(x+1)=272

x=16

x+1=17

Answer 9

13*14; and 16*17

Answer 10

for your first question and second question , to find the integers just use algebra

let x represent the first integer

let x+1 represent the second integer

(x)(x+1)=182

x^2 + x =182

x^2 + x -182 = 0

now u will need to factor it

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

(x-13) = 0 and (x+14) = 0

therefore x can equal 13 and -14, therefore you have two sets of answers

13, 14

-14, -13

and for teh second part you basically follow the same steps

Answer 11

Consecutive integers are two integers whose difference is 1.

Define the first integer as = x

then, the second integer can be x + 1, or it can be x - 1

Either definition will give the same answers

The product of the two integers is:

x (x + 1) = x^2 + x = 182

Set equal to zero and factor

(x + 14)(x - 13) = 182

x = -14 and x + 1 = -13 or,

x = 13 and x + 1 = 14

Check

The second problem is done the same way.

x^2 + x - 272 = 0

(x + 17)(x - 16) = 0

You can get both sets of answers.

Check.