Find the two numbers that multiply to the product number and add to the sum number of the following:
a)Product 563033256; Sum 51895
b)Product -43481220; Sum 28429
c)Product 2545124358; Sum -105619
I tried xy = product and x+y = sum, but it didn't work out... Can someone please help me?
sorry, but I don't get it; how can I have two different solutiuons hen I'm only supposed to have one? Still, thanks.
x+y = sum --->
y = sum - x
product = xy = x(sum-x) ------>
x^2 - sum x + product = 0
x = sum/2 ± sqrt[(sum/2)^2 - product]
There are two solutions because interchanging x and y in the solution will yield another solution. This means that you can take:
x = sum/2 - sqrt[(sum/2)^2 - product]
y = sum/2 + sqrt[(sum/2)^2 - product]
oh, okay, I get it now; thanks!
To find the two numbers that satisfy the given conditions, we can set up a system of equations.
Let's denote the two numbers as x and y.
1) For the first case, we have the product xy = 563033256 and the sum x + y = 51895.
To make it easier to solve the equations, we can rewrite the second equation as x = 51895 - y.
Substituting this value of x into the first equation gives us:
(51895 – y)y = 563033256.
Expanding and rearranging the equation:
51895y – y^2 = 563033256.
Now, we have a quadratic equation:
y^2 – 51895y + 563033256 = 0.
We can solve this quadratic equation to find the values of y. Using factoring, completing the square, or the quadratic formula, we find the values of y as approximately 1631 and 34544.
Substituting these values back into the equation x = 51895 - y, we get the corresponding values of x as approximately 50264 and 17351.
So, in the first case, the two numbers that satisfy the conditions are approximately 50264 and 1631 or 17351 and 34544.
You can follow a similar approach to solve the remaining cases b) and c). By setting up the equations and solving the resulting quadratic equations, you will be able to find the values of x and y.