The product of two consecutive even positive integers is 120. Find the integers.
The product of two consecutive even positive integers is 120. Find the integers.
To find the consecutive even positive integers, let's analyze the problem step by step.
Let's assume that the first even positive integer is "x." As the integers are consecutive, the second even positive integer will be "x + 2".
Given that the product of these two integers is 120, we can set up the equation:
x * (x + 2) = 120
Expanding the equation, we have:
x^2 + 2x = 120
Rearranging the equation in the standard quadratic form, we get:
x^2 + 2x - 120 = 0
Now we can solve this quadratic equation to find the values of x.
To solve this quadratic equation, we can either factor it or use the quadratic formula.
Factoring:
We want two numbers that multiply to -120 and add up to +2. After trying different combinations, we find that +12 and -10 satisfy the conditions.
Therefore, the factored form of the equation becomes:
(x + 12)(x - 10) = 0
Setting each factor equal to zero, we have two possible solutions:
x + 12 = 0 --> x = -12 (not a positive even integer)
x - 10 = 0 --> x = 10
Since we are looking for positive even integers, x = 10 is the solution.
Therefore, the two consecutive even positive integers are 10 and 12.
well, let's see
120 = 10*12