Question

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give me answer of this question please please

Answer 1

$\huge\tt{{\orange{Republic}}_{\blue{Happy}} {\green{Day}}}$



Let, Rehman's present age be $<b>x</b>$ years.

$<u>Before 3 years, his age</u>$

= ( x - 3 ) years

$<u>After 5 years, his age</u>$

= ( x + 5 ) years

A.T.Q.

$\sf{{\dfrac{1}{(x - 3)}} + {\dfrac{1}{(x + 5)}} = {\dfrac{1}{3}}}$


$\sf{{\dfrac{( x + 5 ) + ( x - 3 )}{(x - 3)(x + 5)}} = {\dfrac{1}{3}}}$


$\sf{{\dfrac{x + 5 + x - 3}{x (x + 5) - 3(x + 5)}} = {\dfrac{1}{3}}}$


$\sf{ {\dfrac{2x + 2}{x^2 + 5x - 3x - 15}} = {\dfrac{1}{3}}}$


$\sf{{\dfrac{2x + 2}{x^2 + 2x - 15}} = {\dfrac{1}{3}}}$


Cross Multiplication

3 ( 2x + 2 ) = x² + 2x - 15

6x + 6 = x² + 2x - 15

x² + 2x - 6x - 15 - 6 = 0

x² - 4x - 21= 0

By Middle Term Factorisation

x² - 7x + 3x - 21 = 0

Taking common

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

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

Using Zero Product Rule

x - 7 = 0 and x + 3 = 0

x = 7 and x = - 3

Age can't be negative.

Hence,

$<b><u>Rehman present age is 7 years.</b></u>$