If the sum of two number is 5 and their product equals to 2 how

Edit for formatting:
Let's call the numbers 1/p and 1/q
so our givens are:
1/p+1/q=5
1/p*1/q=2
and we are trying to find 1/(1/p)+1/(1/q)=p+q
From 1/p+1/q=5, we find a common denominator, so
(p+q)/(pq)=5
p+q=5pq

Then from the product equation
1/p*1/q=2
1/(pq)=2
pq=1/2

so plugging back in to p+q=5pq
p+q=5(1/2)
p+q=5/2
and we are done

x + y = 5
xy = 2
solve the system of equations:
x = 2/y
2/y + y = 5
2 + y^2 = 5y
y^2 - 5y + 2 = 0
y^2 - 5y + (5/2)^2 + 2 = (5/2)^2
(y - 5/2)^2 + 2 = 25/4
(y - 5/2)^2 = 33/4
y - 5/2 = √33/2 or y - 5/2 = -√33/2
y = 5/2 + √33/2 or y = 5/2 - √33/2
x = 2 - (5/2 + √33/2) or x = 2 - (5/2 - √33/2)
x = -1/2 - √33/2 or x = -1/2 + √33/2
(x, y) = (-1/2 - √33/2, 5/2 + √33/2) or (x, y) = (-1/2 + √33/2, 5/2 - √33/2)
When you say find the sum of their inverses, do you mean additive or multiplicative inverses?