Question

The sum of 2numbers is 9.Eighteen times the sum of their reciprocals is also 9.Find the numbers.

Answer 1

Answer:

$x = 6 \: \: \: \: \: \: and \: \: \: \: x = 3 \\ \\ one \: number = 6 \\ other \: number = 3$

Step-by-step explanation:

$one \: number = 9 - x \\ 18( \frac{1}{x} + \frac{1}{9 - x} ) = 9 \\ \\ \frac{1}{x} + \frac{1}{9 - x} = \frac{1}{2} \\ \\ \frac{9 - x + x}{x(9 - x)} = \frac{1}{2} \\ \\ \frac{9}{x(9 - x)} = \frac{1}{2} \\ \\ 18 = x(9 - x) \\ \\ 18 = 9x - {x}^{2} \\ \\ {x}^{2} - 9x + 18 = 0 \\ (x - 6)(x - 3) = 0 \\ x = 6 \: \: \: \: \: \: and \: \: \: \: x = 3$

Answer 2

Answer:

Step-by-step explanation: