Question

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

Answer 1

let the two numbers are x and (27-x)

product of the numbers = 182
x(27-x) =182
27x-x² =182

⇒x² -27x +182=0
⇒x²-14x-13x+13*14=0
⇒x(x-14)-13(x-14)=0
⇒(x-14)(x-13)=0
∴x-14 =0 or x-13=0
x=14 or x=13
now the required two numbers are
1) if x= 14 
two numbers are 14,13
2) if x=13
two numbers are (13,14)

Answer 2

Let 1st number be x.
x = 27
Let 2nd number be y.

So, x + y = 27 (Given)
》y = 27 - x
So from now 2nd number is 27 - x

1st no. × 2nd no. = 182 (Given)
x (27 - x) = 182
27x - x square = 182
27x - x square - 182 = 0
x square - 27x + 182 = 0

Then factorize this equation.
You get the answer as 13 and 14.