[tex] \textbf{Given that top ( – 24 ) is the result of a multiplication of two numbers .} [/tex]
Let the numbers are x and ( – 24 / x ) ,
And, also given that bottom ( 5 ) is the result of addition of the same numbers
So,
Sum of both the numbers = 5
[tex] = > x + ( - \dfrac{24}{x} ) = 5 \\ \\ \\ \\ = > \frac{ {x}^{2} - 24}{x} = 5 \\ \\ \\ \\ = > {x}^{2} - 24 = 5x \\ \\ \\ \\ = > {x}^{2} - 5x - 24 = 0[/tex]
Now, a quadratic equation has been formed.
Solving that quadratic equation ,
= > x² - 5x - 24 = 0
= > x² - ( 8 - 3 ) x - 24 = 0
= > x² - 8x + 3x - 24 = 0
= > x( x - 8 ) + 3( x - 8 ) = 0
= > ( x - 8 ) ( x + 3 ) = 0
[tex] \: \: \: \: \: \: \: \: By \: \: Zero \: \: Produc t \: \: Rule ,
[/tex]
= > x = 8 or x = - 3
Hence, taking x = 8
Numbers are x = 8 and ( – 24 / x ) = – 24 / 8 = – 3
Taking x = - 3
Numbers are x = - 3 and ( - 24 / x ) = ( - 24 / - 3 ) = 8
Finally,
We got that numbers are 8 and - 3.
