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The Sum of Natural Number and Its Reciprocal is `65/8` Find the Number - Mathematics

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प्रश्न

The sum of natural number and its reciprocal is `65/8` Find the number 

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उत्तर

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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अध्याय 10: Quadratic Equations - Exercises 5

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आर.एस. अग्रवाल Mathematics [English] Class 10
अध्याय 10 Quadratic Equations
Exercises 5 | Q 17

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