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Quadratic Equations
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30/05/2021 11:18 am
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The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.
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30/05/2021 11:25 am
Let us say, present age of Rahman is x years.
Three years ago, Rehman’s age was (x – 3) years.
Five years after, his age will be (x + 5) years.
Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 1/3.
∴ \(\frac{1}{x-3}+ {1}{x-5}= \frac{1}{3}\)
\(\frac{x+5 + x-3}{(x-3)(x+5)}\) = \(\frac{1}{3}\)
\(\frac{2x+2}{(x-3)(x+5)} = \frac{1}{3}\)
⇒ 3(2x + 2) = (x-3)(x+5)
⇒ 6x + 6 = x2 + 2x – 15
⇒ x2 – 4x – 21 = 0
⇒ x2 – 7x + 3x – 21 = 0
⇒ x(x – 7) + 3(x – 7) = 0
⇒ (x – 7)(x + 3) = 0
⇒ x = 7, -3
As we know, age cannot be negative.
Therefore, Rahman’s present age is 7 years.
This post was modified 5 years ago 2 times by Raavi Tiwari