Question

3.
The sum of reciprocals of Rehman's age (in years) 3 years ago and 5 years from now is 1/3 Find his
present age. ​

Answer 1

Step-by-step explanation:

Given---> Sum of reciprocals of Rehman's age 3years ago and 5years from now is 1/3.

To find ---> Present age of Rehman

Solution---> Let present age of Rehman be x years.

Three years ago Age of Rehman = (x - 3) years

Five years from now age of Rehman

= ( x + 5 )years

ATQ,

Sum of ages 3years ago and 5years from now = 1/3

=> 1 / ( x - 3 ) + 1 / ( x + 5 ) = 1 / 3

=> ( x + 5 ) + ( x - 3 ) / ( x - 3 ) ( x + 5 ) = 1 / 3

=> ( 2x + 2 ) / (x - 3 ) ( x + 5 ) = 1 / 3

=> ( x - 3 ) ( x + 5 ) = 3 ( 2x + 2 )

=> x² + 5x - 3x - 15 = 6x + 6

=> x² + 2x - 15 - 6x - 6 = 0

=> x² - 4x - 21 = 0

Now , we factorize by splitting the middle term, we get,

=> x² - ( 7 - 3 )x - 21 = 0

=> x² - ( 7x - 3x ) - 21 = 0

=> x² - 7x + 3x - 21 = 0

=> x ( x - 7 ) + 3 ( x - 7 ) = 0

=> ( x - 7 ) ( x + 3 ) = 0

If , x + 3 = 0

=> x = -3 ( impossible , age can't be negative )

If , x - 7 = 0

=> x = 7

So , present age of Rehman= 7years

#Answerwithquality

#BAL

Answer 2

Answer:

Please refer the attachment dear