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Question
The sum of a number and its reciprocal is `2 1/30` Find the number.
Solution
Let the required number be x.
According to the given condition,
`x+1/x=2 1/30`
⇒`x^2+1/x=61/30`
⇒ `30x^2+30=61x`
⇒`30x^2-61x+30=0`
⇒`30x^2-36x-25+30=0`
⇒`6x(5x-6)-5(5x-6=0)`
⇒`(5x-6) (6x-5)=0`
⇒`5x-6=0 or x=5/6`
⇒`x=6/5 or x=5/6`
Hence, the required number is` 5/6 or 6/5`
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