Question

separate the number 24 into two parts where the products of the parts is 135. using a quadratic equation and completing the square​

Answer 1

The parts are
`15` and
`9`

Explanation:

Let

x-----> one part

y----> second part

we know that

`x+y=24`

`y=24-x` -----> equation A

`x*y=135` ----> equation B

substitute equation A in equation B

`x*(24-x)=135`

`24x-x^(2)=135\\ \\ x^(2)-24x+135=0`

Completing the square

`x^(2)-24x+135=0`

`x^(2)-24x=-135`

`(x^(2)-24x+12^(2))=-135+12^(2)`

`(x^(2)-24x+144)=9`

rewrite as perfect squares

`(x-12)^(2)=9`

`(x-12)=(+/-)3`

`x=12(+/-)3`

`x1=12(+)3=15`

`x2=12(-)3=9`

The parts are
`15` and
`9`