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Question
The sum of natural number and its reciprocal is `65/8` Find the number
Solution
Let the natural number be x.
According to the given condition,
`x+1/x=65/8`
⇒`(x^2+1)/x=65/8`
⇒`8x^2+8=65x`
⇒`8x^2-65x+8=0`
⇒`8x^2-64x-x+8=0`
⇒`8x(x-8)-1(x-8)=0`
⇒`(x-8)(8x-1)=0`
⇒`x-8=0 or 8x-1=0`
⇒`x=8 or x=1/8`
∴x=8 (x is a natural number)
Hence, the required number is 8.
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