Question

the sum of two numbers is 9 and the sum of their reciprocals is 1/2 find the numbers.

Answer 1

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Answer 2

$\Large{\textbf{\underline{\underline{According\;to\;the\;Question}}}}$

Assumption,

First number = p

Second number = 9 - p

Situation,

1/p + 1/(9 - p) = 1/2

(9 - p) + p/p(9 - p) = 1/2

p(9 - p) = 18

p² - 9p + 18 = 0

Splitting the middle term,

p² - 6p - 3p + 18 = 0

p(p - 6) - 3(p - 6) = 0

(p - 6)(p - 3) = 0

p - 6 = 0 or p - 3 = 0

p = 6, 3

So,

First Number = 6, 3

Second Number = 3, 6