Question

Find two numbers whose sum is 27 and product is 182

Answer 1

ASSUMING
Let the first number be = X
Then the second number = Y
As stated
SUM X + Y = 27 ................. (1)
PRODUCT XY = 182 .................. (2)

From (1)
X = 27 - Y

SUBSITUTE this X value in (2)

(27 - Y) x Y = 182
27Y - Y^2 = 182
Y^2 - 27Y + 182 = 0
Y^2 - 14Y - 13Y + 182 = 0
Y (Y - 14) - 13 (Y - 14) = 0
(Y - 14) (Y - 13) = 0
Y = 14 & Y = 13

CASE 1.
Y = 14 Then X = 27 - 14 = 13
CASE 2.
If Y = 13 Then X = 27 - 13 = 14

Therefore, the two numbers are 13 & 14

Answer 2

Let the first number be x and the second number is 27 - x.
Therefore, their product = x (27 - x)
It is given that the product of these numbers is 182.
Therefore, x(27 - x) = 182
⇒ x2 – 27x + 182 = 0
⇒ x2 – 13x - 14x + 182 = 0
⇒ x(x - 13) -14(x - 13) = 0
⇒ (x - 13)(x -14) = 0
Either x = -13 = 0 or x - 14 = 0
⇒ x = 13 or x = 14
If first number = 13, then
Other number = 27 - 13 = 14
If first number = 14, then
Other number = 27 - 14 = 13
Therefore, the numbers are 13 and 14.