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.
NCERT Class X
Mathematics - Mathematics
Chapter _QUADRATIC EQUATIONS
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4
Let present age be x years
So, 1/(x-3) + 1/(x+5) = 1/3
or, (x + 5 + x - 3)/(x2 + 2x - 15) = 1/3
or, 3(2x + 2) = x2 + 2x - 15
or, 6x + 6 = x2 + 2x - 15
or, x2 - 4x - 21 =0
or, x2 - 7x + 3x - 21 = 0
or, (x-7)(x+3) = 0
So, x = 7 (Age cannot be negative)
So, Rehman's age is 7 years
So, 1/(x-3) + 1/(x+5) = 1/3
or, (x + 5 + x - 3)/(x2 + 2x - 15) = 1/3
or, 3(2x + 2) = x2 + 2x - 15
or, 6x + 6 = x2 + 2x - 15
or, x2 - 4x - 21 =0
or, x2 - 7x + 3x - 21 = 0
or, (x-7)(x+3) = 0
So, x = 7 (Age cannot be negative)
So, Rehman's age is 7 years
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