Question

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

Answer 1

Answer:

let numbers be x and y

x+y=27

xy=182

first find x-y

${(x - y)}^{2} = {(x + y)}^{2} - 4xy$

${(x - y)}^{2} = {27}^{2} - 4\times182$

${(x - y)}^{2} = 729 - 728$

$= 1$

$(x - y) = 1$

on adding (x+y) and(x-y)

$x + y + x - y = 27 + 1$

$2x = 28 \\ x = 28 \div 2 = 14$

$y = 27 - 14 = 13$

Answer 2

Solution:

Sol. Let one number be x, then other number be 27 - X

ATQ

⇒ x (27-x) = 182

⇒ x²- 27x + 182 = 0

⇒ x² -14x- 13x + 182 = 0

⇒ x (x - 14) - 13 (x - 14) = 0

⇒(x - 13) (x - 14) = 0

⇒ x - 13 = 0

or x- 14=10

⇒ x = 13

or x = 14

Hence, the numbers are 13 and 14.