separate the number 24 into two parts where the products of the parts is 135. using a quadratic equation and completing the square
Accepted Solution
A:
Answer:The parts are [tex]15[/tex] and [tex]9[/tex]Step-by-step explanation:Letx-----> one party----> second partwe know that[tex]x+y=24[/tex][tex]y=24-x[/tex] -----> equation A[tex]x*y=135[/tex] ----> equation Bsubstitute 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]