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  • The sum of two numbers is 15 if their reciprocals is 3/10 find the two number using quadratic formula

The sum of two numbers is 15 if their reciprocals is 3/10 find the two number using quadratic formula

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$ Assume two numbers are x,y. $ \\\\ ATQ \ \ x + y = 15...(i) \\\\ \frac{1}{x} + \frac{1}{y} = \frac{3}{10} \\\\ \frac{x+y}{xy} = \frac{3}{10} \\\\10(x+y) = 3xy \\ 3xy = 150 \\ xy = 50...(ii) \ \ \ \text{From equation (i)}\\ x(15-x) = 50 \\ x^2 - 15x + 50 =0 \\ x^2 - 10x - 5x + 50 =0 \\ x(x-10) - 5(x-10) =0 \\ (x-10)(x-5) = 0 \\ x = 10 \ or \ x = 5 \\ y = 5 \ or \ y = 10

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Ravindra Pindel

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