xy = 3/2 implies that y = 3 / [ 2x]
So....plugging this into the second function and get that
10x + (3/5)(3/[2x]) =
10x + 9 / (10x)
If you haven't had Calculus....we can find the minimum of this curve : https://www.desmos.com/calculator/nbecr6spbo
The minimum value occurs at x = 3/10 and the minimum is y = 6
If you have had Calculus....let the function be
y = 10x + (9/10)x^(-1) take the derivative and set to 0
y ' = 10 - (9/10)x^(-2) = 0
10 = (9/10)x^(-2) rearrange as
x^2 = 9/100 take the positive root (since x must be positive)
x = 3/10
Taking the second derivative we have
y " = (18/10)x^(-3)
Putting 3/10 into this produces a positive.....this indicates a minimum at x = 3/10
And y = 10(3/10) + (9/10)/ (3/10) =
3 + (9/10) (10/3) =
3 + 9/3 =
6 !!!