Question

The sum of reciprocals of rehman's age 3 years ago and 5 years from now is1/3.find his present age

Answer 1

$\bold{\huge{Hay!!}}$


$\bold{Dear\:user!!}$



$\bold{\underline{Question-}}$

The sum of reciprocals of rehman's age 3 years ago and 5 years from now is1/3.find his present age



$\bold{\underline{Answer-}}$




$\bold{Your\:answer\:is\:\:(7\:years)}$





$\bold{\underline{Explanation-}}$According to the question we know that the sum of reciprocals of rehman's age 3 years ago and 5 years from now 1/3


So,


Let, the rehaman present age is x


then,


Three years ago Rehaman age is x - 3


and, After five years Rehaman and is x + 5



So,

Three years ago rehaman age + after five years rehaman age = 1/3


now, putting the above values we get



$\frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3} \\ \\ \\ \frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3} \\ \\ \\ {x}^{2} + 2x - 15 = 6x + 6 \\ \\ \\ \\ {x}^{2} - 4x - 21 = 0$



For quadratic equations we we have a = 1 ,
b = - 4 , c = -21



Now, using the formula of quadratic equations

b² - 4ac

=> -4² - 4 × 1 × -21

=> 16 + 84 = 100


Here, 100>0 so,



using =$AS \: \: x = \frac{ - b ± \sqrt{ {b}^{2} - 4ac } }{2a}$



$\: \: x = \frac{ 4±\sqrt{ 100} }{2} = \frac{4 ± 10}{2} \:$



if we let minus sine then,


x => (4 - 10 ) / 2

x => ( - 6) / 2

x => -3



if we let plus sine then,



x => (4 + 10) / 2

=> 14 / 2

=> 7



so, The Rehaman's age is 7



because the age of a person can't be negative





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