What is the best way for solving this question of quadratic equations, It is very important question for class 10th. How i solve by easy way 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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# 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. Q.4

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Let us say, present age of Rehman is

xyears.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.

∴ 1/

x-3 + 1/x-5 = 1/3(x+5+x-3)/(x-3)(x+5) = 1/3(2

x+2)/(x-3)(x+5) = 1/3⇒ 3(2

x+ 2) = (x-3)(x+5)⇒ 6

x+ 6 =x^{2}+ 2x– 15⇒

x^{2}– 4x– 21 = 0⇒

x^{2}– 7x+ 3x– 21 = 0⇒

x(x– 7) + 3(x– 7) = 0⇒ (

x– 7)(x+ 3) = 0⇒

x= 7, -3As we know, age cannot be negative.

Therefore, Rehman’s present age is 7 years.