Question

find the number whose sum is 27 and product is 182​

Answer 1

Let the two numbers be x and y

We have

x + y = 27

==> x = 27 - y ( on transposition) - - - (1)

Also,

x ( y) = 182

27- y (y) = 182 ( by 1)

27y - y^2 = 182

y^2 - 27y + 182 = 0

By factorisation

y^2 - 14y - 13y + 182 = 0

y ( y- 14) - 13 (y - 14) = 0

(y-13) (y - 14) =0

y= 13 and y = 14

When y = 13 in (1)

x = 27 - 13

x = 14

When y = 14 in (1)

x = 27 - 14

x = 13

i. e the two numbers are 13 and 14.

Hope it helps you ☺️