The two numbers whose sum is 27 and product is 182 are ____.

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Detailed Solution

Let the two numbers be x and y. Given that the sum is 27 and the product is 182.
We have,

x + y = 27

y = 27 − x

… (1)

x y = 182

… (2)
Substitute (1) in (2), and we have

x (27 − x) = 182 27 x − x 2 = 182 x 2 − 27 x + 182 = 0 x 2 − 14 x − 13 x + 182 = 0 x (x − 14) − 13 (x − 14) = 0 (x − 14) (x − 13) = 0

We have,

x − 14 = 0 x = 14

(or)

x − 13 = 0 x = 13

Substitute the above values in the equation (1), and we have

y = 27 − 14 = 13 y = 27 − 13 = 14

Hence, the two numbers are

(14, 13)

and

(13, 14)

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