Question

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

Answer 1

Let the two numbers be $a,b$

$a+b=27b=27-a$

Product of numbers is $180$

$ab=180$

$a(27-a)=180$

$27a-a^2=180$

$a^2-27a+180=0$

$a^2-12a-15a+180=0$

$a(a-12)-15(a-12)=0$

$(a-12)(a-15)=0$

$a=12,15$

So the numbers are $12,15$