Question

The product of two positive numbers is $120$ and the sum of their square is $289$. The difference between them is:

• A. $7$
• B. $-7$
• C. $2$
• D. $14$

Answer 1

The correct option is A $7$

$xy=120$
$x^2+y^2=289$
$(x+y{)}^2-2xy=289$
$\Rightarrow (x+y{)}^2=289-2\times 120=49\Rightarrow x+y=7$
Using $y=\frac{120}{x}\Rightarrow x+\frac{120}{x}=7$
$x^2-7x+120=0$
$(x+8)(x-15)=0\Rightarrow x=15$ & $y=8$
$\therefore$ Difference $=15-8=7$