Answer: The numbers are 2 and 2.5
Explanation:
Let one number be "x" and another "y", Note: 9/2 = 4.5 [in decimal form]
[tex]\rule{185}{2}[/tex]
Their product :
[tex]\hookrightarrow \sf x \ \cdot \ y = 5[/tex]
[tex]\hookrightarrow \sf x = \dfrac{5}{y} \quad \ \ \leftarrow \quad equation _1[/tex]
Their sum :
[tex]\hookrightarrow \sf x + y = 4.5[/tex]
[tex]\hookrightarrow \sf x = 4.5-y \quad \ \ \leftarrow \ equation_2[/tex]
Solve them simultaneously:
[tex]\rightarrow \sf 4.5 - y = \dfrac{5}{y}[/tex]
cross multiply
[tex]\rightarrow \sf y(4.5 - y) = 5[/tex]
distribute inside parenthesis
[tex]\rightarrow \sf -y^2 +4.5y - 5 = 0[/tex]
multiply by -1
[tex]\rightarrow \sf y^2 -4.5y + 5 = 0[/tex]
factor them out
[tex]\rightarrow \sf ( y - 2.5)(y - 2)= 0[/tex]
set to 0
[tex]\rightarrow \sf y = 2.5, \ 2[/tex]
Another number:
When one number is 2.5, then another: 4.5 - 2.5 = 2
When one number is 2, then another: 4.5 - 2 = 2.5
- Hence, the numbers are 2.5 and 2
Check:
- Sum: 2 + 2.5 = 4.5 or 9/2
