Question

Question 3
Find two numbers whose sum is 27 and product is 182.

Answer 1

Let the first number be $x$ and the second number is $27-x$.
Therefore, their product = $x(27-x)$
It is given that the product of these numbers is $182$.
Therefore, $x(27-x)=182$
$\Rightarrow x^2-27x+182=0$
(Splitting the middle term -27x as -13x-14x because $-13x\times -14x=182x^2$)
$\Rightarrow x^2-13x-14x+182=0$
$\Rightarrow x(x-13)-14(x-13)=0$
$\Rightarrow (x-13)(x-14)=0$
Either $x-13=0orx-14=0$
$\Rightarrow x=13orx=14$
If first number = $13$, then
Other number = $27-13=14$

Therefore, the numbers are $13$ and $14$.