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

Explanation

Let the required numbers be x and `(27-x)`. Then,
`x(27-x)=182`
`implies" "27x-x^(2)=182impliesx^(2)-27x+182=0`
`implies" "x^(2)-13x-14x+182=0`
`implies" "x(x-13)-14(x-13)=0`
`implies" "(x-13)(x-14)=0`
`implies" "x-13=0" or "x-14=0`
`implies" "x=13" or "x=14.`
Hence, the required numbers are 13 and 14.