Question

The sum of reciprocals of reman's ages 3 years ago and 5 years from now is 1/3. Find his present age.

Answer 1

Answer:

I hope this picture would help you

Answer 2

X = 7

Step-by-step explanation:

Let the present age be  x

so the reciprocal of x is = $\frac{1}{x}$

His age was 3 years age = $(x-3)$

so the reciprocal of age 3 year age =  $\frac{1}{x-3}$

His age is years now = $(x+5)$

so the reciprocal of age 5 years now = $\frac{1}{x+5}$

According to question

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

by using cross multiplication

$6x+6=x^2+2x-15\\x^2+2x-15-6x-6=0\\x^2-4x-21=0$

By using middle term splitting

$(x^2+3x)-(7x-21)=0\\x(x+3)-7(x+3)\\\\x=7 \\ x\neq 3$(because age are not in negative)