Question

the sum of the reciprocals of humans age in years 3 years ago and 5 years from now is 1 by 3 find his present age

Answer 1

Let his current age be 'x'.

Therefore,

Age 3 yrs ago=x-3

Age 5 yrs from now=x+5

The required eqn is,

1/x-3+1/x+5=1/3;

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

2x+2/x^2+5x-3x-15=1/3

2x+2/x^2+2x-15=1/3

6x+6=x^2+2x-15

x^2-4x-21=0

x^2-7x+3x-21=0

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

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

Therefore,

x=7,-3

But since age cannot be negative, his age is 7yrs