Question

the sum of the reciprocals of Robbins age is your tree or ago and 5 year from now is 1 by 3 find his present age​

Answer 1

Correct question: The sum of reciprocals of Robbins age three years ago and 5 years from now is 1/3. Find his present age.

Answer:

$\large{\underline{\boxed{\sf Robbin's \: age = 7 \: years. }}}$

Step-by-step explanation:

Let the present age of robbin be x years.

So, Robbin's age 3 years ago = (x - 3) years.

And, the age of Robbin 5 years from now = (x + 5) years.

According to the question ;

Equation formed:

$\boxed{ \bf \dfrac{1}{x - 3} + \dfrac{1}{x + 5} = \dfrac{1}{3} }$

On solving the above equation ;

$\sf \frac{1}{x - 3} + \frac{1}{x + 5} = \frac{1}{3} \\ \\ \implies \sf \frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3} \\ \\ \implies \sf \frac{x + 5 + x - 3}{x {}^{2} + 5x - 3x - 15} = \frac{1}{3} \\ \\ \implies \sf \frac{2x + 2}{x {}^{2} + 2x - 15} = \frac{1}{3} \\ \\ \bf on \: cross-multiplying \: both \: sides : \\ \\ \implies \sf x {}^{2} + 2x - 15 = 3(2x + 2) \\ \\ \implies \sf {x}^{2} + 2x - 15 = 6x + 6 \\ \\ \implies \sf {x}^{2} + 2x - 15 - 6x - 6 = 0 \\ \\ \implies \sf {x}^{2} - 4x - 21 = 0$

Here, we got an equation, it can be solved by splitting the middle term. Here we go;

$\implies \sf {x}^{2} - 4x - 21 = 0\\ \\ \implies \sf x {}^{2} - 7x + 3x - 21 = 0 \\ \\ \implies \sf x(x - 7) + 3(x - 7) = 0 \\ \\ \implies \sf (x - 7)( x+ 3) = 0$

By zero product rule ;

⇒ x = 7 or x = - 3

Since, age can not be negative. We can neglect (-3).

Hence, the age of Robbin is 7 years.

Answer 2

Answer:

Please refer the attachment dear

Step-by-step explanation:

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