Question

find the two numbers whose sum is 27 and product is 182

Answer 1

Let the one number be x.

Another number will be ( 27 - x ).

A.T.Q.

( x ) ( 27 - x ) = 182

27x - x² = 182

x² - 27x + 182 = 0

By Middle Term factorisation

x² - 14x - 13x + 182 = 0

x ( x - 14 ) - 13 ( x - 14 ) = 0

( x - 14 ) ( x - 13 ) = 0

Using Zero Product Rule

x - 14 = 0 and x - 13 = 0

x = 14 and x = 13

$<u>Case I</u>$ : When x = 14

One number = x = 14

Another number = 27 - x = 27 - 14 = 13

$<u>Case II</u>$ : When x = 13

One number = x = 13

Another number = 27 - x = 27 - 13 = 14

Hence, $<b>the required numbers are 13 and 14.</b>$

Answer 2

Answer:

13+14=27

13×14=182