Question

The sum of the reciprocals of swamy s age 3years ago and 5 years from now is 1/3 prepare the quadratic equation in the variable Z to the above statement



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Answer 1

Answer:

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Step-by-step explanation:

$so \: let \: swamy \: present \: age \: be \: z \: years \\ wherein \: his \: age \: three \: years \: ago \: be \: \\ (z - 3) \: years \: \\ and \: that \: of \: 5 \: years \: from \: now \: be \: \\ (z + 5) \: years \\ \\ according \: to \: given \: condition \\ \\ \frac{1}{z - 3} + \frac{1}{z + 5} = \frac{1}{3} \\ \\ \frac{z + 5 + z - 3}{(z + 5)(z - 3)} = \frac{1}{3} \\ \\ \frac{2z + 2}{z {}^{2} - 3z + 5z - 15} = \frac{1}{3} \\ \\ 3(2z + 2) = z {}^{2} + 2z - 15 \\ \\ 6z + 6 = z {}^{2} + 2z - 15 \\ \\ z {}^{2} - 4z - 21 = 0 \\ \\ z {}^{2} - 7z + 3z - 21 = 0 \\ \\ z(z - 7) + 3(z - 7) = 0 \\ \\ (z + 3)(z - 7) = 0 \\ \\ z = 7 \: \: or \: \: z = - 3 \\ \\ but \: as \: age \: is \: never \: negative \\ z = - 3 \: \: is \: absurd \\ \\ hence \: \: z = 7$