Question

Find two numbers, whose sum is $27$ and product is $182$.

Answer 1

Let $x$ and $y$ be two numbers

Given, $x+y=27$ ............(1)

and $xy=182$ .............(2)

From (1), we get $x=27-y$

Put $x=27-y$ in (2) we get,

$(27-y)y=182\Rightarrow 27y-y^2=182\Rightarrow y^2-27y+182=0$

$\Rightarrow (y-14)(y-13)=0$

$\Rightarrow y=14$ or $y=13$

$\therefore$ if $y=14$ then $x=13$ and if $y=13$ then $x=14$

Two numbers are $13$ and $14$