The product of two consecutive intergers is 56. Find the intergers.
7 and 8. 7times8=56
let the integers be x and x+1
x(x+1) = 56
x^2 + x - 56 = 0
(x+8)(x-7) = 0
x = -8 or x = 7
the 2 number are either 7 and 8
or -8 and -7
the sum of three consecutive even integers is 780. how do you figure that out.
To find the two consecutive integers, we can set up an equation. Let's call the first integer "x". The second consecutive integer would be "x + 1" since they are consecutive.
The problem states that the product of these two consecutive integers is 56, so we can write the equation:
x * (x + 1) = 56
To solve this equation, we can expand the expression:
x^2 + x = 56
Rearranging the equation so that it's in standard quadratic form gives us:
x^2 + x - 56 = 0
Now, we can solve this quadratic equation by factoring or by using the quadratic formula. Let's use factoring:
We need to find two numbers that multiply to -56 and add up to 1. The numbers 8 and -7 have a product of -56 and a sum of 1. So, we can rewrite the quadratic equation as:
(x + 8)(x - 7) = 0
From this factored form, we can see that the two possible values for x are -8 and 7.
Therefore, the two consecutive integers are -8 and -7, or 7 and 8.