Question

If $xy=144,x+y=30$ and $x>y$, compute the value of $x-y$.

• A. $4$
• B. $6$
• C. $18$
• D. $22$
• E. $24$

Answer 1

The correct option is C $18$

Given, $xy=144$

$x=\frac{144}{y}$..... (1)

$x+y=30$

Put the value of $x$ from (1)

$\Rightarrow \frac{144}{y}+y=30$

$\Rightarrow \frac{144+y^2}{y}=30$

$\Rightarrow 144+y^2=30y$

$\Rightarrow y^2-30y+144=0$

$\Rightarrow y^2-24y-6y+144=0$

$\Rightarrow y(y-24)-6(y-24)=0$

$\Rightarrow (y-24)(y-6)=0$

$\Rightarrow y=24,6$

AS $x>y$, so $y=6$

Put the value of $y$ in (1), we get

$x=\frac{144}{6}=24$

$\therefore x-y=24-6=18$