Question

The sum of two number is 9 and sum of their reciprocal is1/2.find no

Answer 1

Answer:

sum of two number = 9

let the numbers be x and y

Therefore ,

$x + y = 9 \: ........equ(1) \\multiply \: by \: 2 \\ 2x + 2y = 18.......equ(2)$

sum of the reciprocals = 1/2

$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{2} \\ \therefore \: \dfrac{x + y}{xy} = \frac{1}{2} \\ \therefore \: 2(x + y) = xy \\ \implies \: 2x + 2y = xy \: ......equ(3)$

from equation 2 and 3

$xy = 18 \\ \implies \: x = \frac{18}{y} ......equ(4)$

using equation 1

$\dfrac{18}{y} + y = 9 \\ \implies \: {y}^{2} - 9y + 18 = 0 \\ {y}^{2} - 6y - 3y + 18 = 0 \\ y(y - 6) - 3(y - 6) = 0 \\ (y - 6)(y - 3) = 0 \\ \implies \: y = 6 \: or \: y = 3$

Substituting equ(1) , We get

therefore the value of x = 3 or 6

Answer 2

Refers to attachment ♡~