Question

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

Answer 1

Let the first number be $x$ then the second number will be $27-x.$

$x(27-x)=182$

$\Rightarrow 27x-x^2=182$

$\Rightarrow x^2-27x+182=0$

$\Rightarrow x^2-13x-14x+182=0$

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

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

$\Rightarrow x=14,13$

If the first number is $14,$ then the second number is $13$ and if the first number is $13,$ then the second number is $14$.