The Product of 2 consecutive odd numbers is 783. What are the numbers?
square root(783) = 27.9821372
To find the two consecutive odd numbers whose product is 783, we can set up an equation.
Let's assume the first odd number is x. Since they are consecutive odd numbers, the second odd number would be x + 2 (as the difference between consecutive odd numbers is 2).
Now, we can create an equation using the given information:
x * (x + 2) = 783
Expanding the equation:
x^2 + 2x = 783
Rearranging the equation to a quadratic form:
x^2 + 2x - 783 = 0
Now we can solve this quadratic equation for the value of x. There are a few methods to solve quadratic equations, but let's use factoring here:
To factor the quadratic equation, we need to find two numbers whose sum is 2 and whose product is -783. After some trial and error, we find that the two numbers are 29 and -27:
(x + 29)(x - 27) = 0
Setting each factor equal to zero and solving for x:
x + 29 = 0 or x - 27 = 0
x = -29 or x = 27
So, we have two possible values for x: -29 and 27.
Since we are looking for odd numbers, we can discard the negative value (-29) and consider only the positive value (27). Therefore, the two consecutive odd numbers whose product is 783 are 27 and 29.