Answer:
The parts are [tex]15[/tex] and [tex]9[/tex]
Step-by-step explanation:
Let
x-----> one part
y----> second part
we know that
[tex]x+y=24[/tex]
[tex]y=24-x[/tex] -----> equation A
[tex]x*y=135[/tex] ----> equation B
substitute equation A in equation B
[tex]x*(24-x)=135[/tex]
[tex]24x-x^{2}=135\\ \\ x^{2}-24x+135=0[/tex]
Completing the square
[tex]x^{2}-24x+135=0[/tex]
[tex]x^{2}-24x=-135[/tex]
[tex](x^{2}-24x+12^{2})=-135+12^{2}[/tex]
[tex](x^{2}-24x+144)=9[/tex]
rewrite as perfect squares
[tex](x-12)^{2}=9[/tex]
[tex](x-12)=(+/-)3[/tex]
[tex]x=12(+/-)3[/tex]
[tex]x1=12(+)3=15[/tex]
[tex]x2=12(-)3=9[/tex]
The parts are [tex]15[/tex] and [tex]9[/tex]
