The sum of two natural numbers is 9 and the sum of their reciprocal is $\frac{1}{2}$ . Find the numbers.

Open in App

Solution

Let one number be x
and other number be 9-x

sum of their reciprocal is

$1 over x plus fraction numerator 1 over denominator 9 minus x end fraction equals 1 half fraction numerator 9 minus x plus x over denominator x open parentheses 9 minus x close parentheses end fraction equals 1 half fraction numerator 9 over denominator x open parentheses 9 minus x close parentheses end fraction equals 1 half$
x(9-x)=18

x(x-6)-3(x-6)=0
(x-6)(x-3)=0
x=6,3
when one=6, other=3

Suggest Corrections

Similar questions

9

\frac{1}{2}

The sum of two numbers is 9. If the sum of their reciprocals is $\frac{1}{2}$ , find the numbers.

The sum of two natural numbers is 15 and the sum of their reciprocals is $\frac{3}{10}$ . Find the numbers.

\frac{1}{2}

8

\frac{2}{15}

Join BYJU'S Learning Program