Question

The sum of two numbers is 48 and their product is 432. Find the numbers.

Answer 1

SOLUTION :  

Given : Sum of two Numbers is 48 and their products is 432.

Let the first number be x  & other no. be (48 - x)

A.T.Q

( x ) ( 48 - x ) = 432  

48x - x² = 432  

x² - 48x + 432 = 0  

x² - 36x - 12x + 432 = 0

x( x - 36) - 12( x - 36) = 0

x - 12 = 0  or  x - 36 = 0  

x = 12 or  x = 36  

Case 1 :  

If  x =  12 , then the two Numbers  are 12 and (48 - 12) = 36  

Case 2 :  

If x = 36 , then the two Numbers are 36 and (48 - 36) = 12

Hence, the two numbers be 12 & 36 .

HOPE THIS  ANSWER WILL HELP YOU..

Answer 2

Solution :

Given sum of two numbers = 48

Let the first number = x

Second number = 48 - x

Product of these numbers = 432

=> x( 48 - x ) = 432

=> 48x - x² = 432

=> x² - 48x + 432 = 0

Splitting the middle term, we get

=> x² - 36x -12x + 432 = 0

=> x( x - 36 ) - 12( x - 36 ) = 0

=> ( x - 36 )( x - 12 ) = 0

=> x - 36 = 0 or x -12 = 0

=> x = 36 or x = 12

Therefore ,

Required Numbers are ,

i ) If first number ( x ) = 36 ,

Second number = 48 - x

= 48 - 36 = 12

ii ) If first number ( x ) = 12

Second Number = 48 - x

= 48 - 12

= 36

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