The sum of two numbers is 18. the sum of the reciprocal of those numbers is 1/4. the numbers are

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The sum of two numbers is 18 . The sum of their reciprocals is 1 / 4 . Find the numbers.

Solution

Let one of the number be x then other number is (18 − x).

Then according to question,

1x+118-x=14⇒18-x+xx(18-x)=14⇒18×4=18x-x2⇒72=18x-x2⇒x2-18x+72=0⇒x2-12x-6x+72=0⇒x(x-12)-6(x-12)=0⇒(x-6)(x-12)=0⇒x-6=0 or x-12=0⇒x=6 or x=12

Since, x being a number,

Therefore,

When x=12 then another number will be

18-x=18-12=6

And when x=6 then another number will be

18-x=18-6=12

Thus, the two numbers are 6 and 12.

Mathematics

RD Sharma (2016)

Standard X