Greetings from Brasil...
According to the statement of the question, we can assemble the following system of equation:
X · Y = - 2 i
X + Y = 7 ii
isolating X from i and replacing in ii:
X · Y = - 2
X = - 2/Y
X + Y = 7
(- 2/Y) + Y = 7 multiplying everything by Y
(- 2Y/Y) + Y·Y = 7·Y
- 2 + Y² = 7X rearranging everything
Y² - 7X - 2 = 0 2nd degree equation
Δ = b² - 4·a·c
Δ = (- 7)² - 4·1·(- 2)
Δ = 49 + 8
Δ = 57
X = (- b ± √Δ)/2a
X' = (- (- 7) ± √57)/2·1
X' = (7 + √57)/2
X' = (7 - √57)/2
So, the numbers are:
(7 + √57)/2
and
(7 - √57)/2
