Two positive intergers have a sum of 17 and a product of 66.What are the intergers?
I'm sure there's a formula for this -- but let's try common sense trial and error.
9 * 8 = 72
7 * 10 = 70
6 * 11 = ?
This is what I have
x=1st interger
17-x= 2nd interger
equation:
x(x-17)=66
x^2-17x-66
then I have to factor it but I don't know the factors that is what I need help with finding that
To find the two positive integers, we can start by setting up some equations based on the given information.
Let's assume the first positive integer is represented by "x" and the second positive integer is represented by "y". According to the problem, we have two pieces of information:
1. The sum of the two positive integers is 17: x + y = 17.
2. The product of the two positive integers is 66: x * y = 66.
Now, we have a system of equations consisting of two equations with two variables. We can solve this system to find the values of x and y.
One way to solve this system of equations is by substitution. We can solve the first equation for x in terms of y, and then substitute it into the second equation.
From the first equation, x = 17 - y.
Substituting this expression of x into the second equation: (17 - y) * y = 66.
Expanding the equation: 17y - y^2 = 66.
Rearranging the equation to make it a quadratic equation: y^2 - 17y + 66 = 0.
Now we have a quadratic equation, and we can solve it by factoring or using the quadratic formula.
Factoring the quadratic equation gives us: (y - 11)(y - 6) = 0.
Setting each factor equal to zero gives us two possible values for y: y - 11 = 0 (y = 11) or y - 6 = 0 (y = 6).
We have found two values for y, but we need to make sure they are positive integers.
Checking the first value, y = 11, we can substitute it back into the first equation to find x: x + 11 = 17, x = 6.
Checking the second value, y = 6, we can again substitute it into the first equation to find x: x + 6 = 17, x = 11.
So, we have two pairs of positive integers that satisfy the given conditions: (6, 11) and (11, 6).