Answer:
The two numbers are 5.73 and 2,27
Step-by-step explanation:
Let the two numbers be x and y
[tex]x + y = 8[/tex]
[tex]xy = 13[/tex]
Make x the subject in the first equation
[tex]x = 8 - y[/tex]
Substitute 8 - y for x in the second equation
[tex](8-y)*y = 13[/tex]
Open brackets
[tex]8y - y^2 = 13[/tex]
Equate to 0
[tex]y^2 - 8y + 13 = 0[/tex]
Solve using quadratic formula
[tex]y = \frac{-b \± \sqrt{b^2 - 4ac}}{2a}[/tex]
Where
[tex]a = 1[/tex] [tex]b = -8[/tex] [tex]c = 13[/tex]
So:
[tex]y = \frac{-(-8) \± \sqrt{(-8)^2 - 4*1*13}}{2*1}[/tex]
[tex]y = \frac{8 \± \sqrt{64 -52}}{2}[/tex]
[tex]y = \frac{8 \± \sqrt{12}}{2}[/tex]
[tex]y = \frac{8 \± 3.46}{2}[/tex]
Split
[tex]y = \frac{8 + 3.46}{2}[/tex] or [tex]y = \frac{8 - 3.46}{2}[/tex]
[tex]y = \frac{11.46}{2}[/tex] or [tex]y = \frac{4.54}{2}[/tex]
[tex]y = 5.73[/tex] or [tex]y = 2.27[/tex]
Recall that
[tex]x = 8 - y[/tex]
When [tex]y = 5.73[/tex]
[tex]x = 8 - 5.73[/tex]
[tex]x = 2.27[/tex]
When [tex]y = 2.27[/tex]
[tex]x = 5.73[/tex]
Hence, the two numbers are 5.73 and 2,27
