Questions of exercise 4.3

Find the roots of the following equations 

            

(a)  X -   1    = 3     (b)    1     -       1      =   11 
               X                    X+4         X-7           30

Question No.4...The sum of the reciprocals of Rehman's age(in years) three years ago and five years from now will be 1/3. Find his present age.

Solution: Let Rehman's present age= x
   
                  3 years ago
             Rehman's age=x-3

                5 years After
              Rehman's age= x+5



By the question

   1     +          1    =   1
x-3             x+5        3
Cross multiplication
x+5 + x -3     =    1 
(x-3)(x+5)           3

   2x + 2               =    1 
x² + 5x-3x -15       3

   2x + 2        =      1 
x² +2x -15         3

x² +2x -15   = 6x + 6

x² +2x -15 - 6x - 6 =0

x² - 4x - 21 = 0
Now splitting the middle term

x² -7x +3x -21 = 0

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

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

Either x-7 =0     or    x+3=0
         =>   x=7     or     x = -3  (Rejected)
                           because age can't be negative

Hence Rehman's present age = 7years