If xy=7 and x-y=5 then x2 y-xy2=
x^2y - xy^2
=xy(x-y)
= 7(5) = 35
To find the value of x^2y - xy^2, we first need to find the values of x and y.
We are given two equations:
1) xy = 7
2) x - y = 5
To solve for x and y, we can use the method of substitution or elimination. Let's solve it using the method of substitution.
From equation 2, we can rearrange it to obtain the value of x in terms of y:
x = y + 5
Now substitute this value of x into equation 1:
(y + 5)y = 7
Expanding the equation:
y^2 + 5y = 7
Rearranging the equation:
y^2 + 5y - 7 = 0
This is a quadratic equation in terms of y. We can solve this equation by factoring, completing the square, or using the quadratic formula.
Using the quadratic formula:
y = (-5 ± √(5^2 - 4(1)(-7))) / (2(1))
y = (-5 ± √(25 + 28)) / 2
y = (-5 ± √53) / 2
So we have two potential values for y:
y = (-5 + √53) / 2
y = (-5 - √53) / 2
Now that we have the values of y, we can substitute them back into equation 2 to find the corresponding values of x.
For y = (-5 + √53) / 2:
x = (-5 + √53) / 2 + 5
x = (-5 + √53 + 10) / 2
x = (5 + √53) / 2
For y = (-5 - √53) / 2:
x = (-5 - √53) / 2 + 5
x = (-5 - √53 + 10) / 2
x = (5 - √53) / 2
Now that we have the values of x and y, we can substitute them into x^2y - xy^2:
For y = (-5 + √53) / 2 and x = (5 + √53) / 2:
x^2y - xy^2 = [(5 + √53) / 2]^2 * (-5 + √53) / 2 - (5 + √53) / 2 * [(-5 + √53) / 2]^2
By simplifying the expression, the final result can be obtained.