Question

Two numbers are such that their sum is $18$ and product is $45$. Find the difference of these two numbers.

Answer 1

Let two numbers be $x$ and $y$.

$xy=45\Rightarrow x=\frac{45}{y}............\left(1\right)$

$x+y=18\Rightarrow \frac{45}{y}+y=18$

or, $45+y^2=18y$

or, $y^2-18y+45=0$

or, $y^2-15y-3y+45=0\Rightarrow (y-3)(y-15)=0$

$\therefore y=3\Rightarrow x=15$ and $y=15\Rightarrow x=3$.

Difference $=15-3=12$ Ans