Question

If xy= 144, x +y =30, and x>y what is the value of x-y

Answer 1

$xy=144\implies y=\dfrac{144}x$
$x+y=30\implies x+\dfrac{144}x=30$

$\implies x^2-30x+144=(x-24)(x-6)=0$
$\implies x=24\text{ or }x=6$

In the case of $x=24$, we have $y=\dfrac{144}{24}=6$, so that $x-y=18$.

On the other hand, if $x=6$, then $y=144$. But this breaks the condition that $x>y$.