production of two numbers is 19951 and sum of those two numbers is 280 (x+y=280).Without assigned those numbers find difference between them (x-y=?)
well,
(x+y)^2 - (x-y)^2 = 4xy
So, (x-y)^2 = 280^2 - 4*19951
Where did u get the 4(number 4), when u did 4xy?
To find the difference between two numbers without knowing the exact values, we can use a system of equations and algebraic manipulation.
Let's first assign variables to the two numbers. Let's call the first number x and the second number y.
Given that the production of the two numbers is 19951, we can write the equation:
x * y = 19951 [Equation 1]
Also, given that the sum of the two numbers is 280, we can write the equation:
x + y = 280 [Equation 2]
To find the difference between x and y, we need to find x - y.
Now, let's solve the system of equations to find the values of x and y.
From Equation 2, we can express x in terms of y:
x = 280 - y [Equation 3]
Substituting Equation 3 into Equation 1, we can eliminate x:
(280 - y) * y = 19951
Expanding and rearranging the equation gives us:
280y - y^2 = 19951
Rearranging further and setting the equation to zero, we have:
y^2 - 280y + 19951 = 0
Now, we can solve this quadratic equation for y using factoring, completing the square, or the quadratic formula.
Once we find the value(s) of y, we can substitute it back into Equation 3 to find the corresponding value(s) of x.
Then, we can calculate the difference between x and y by subtracting y from x (x - y).
Please note that solving the quadratic equation may result in one or two distinct values for y. Each solution will yield a different difference between x and y.