The difference between a natural number and twice its reciprocal is 477, then the number is
A
2
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B
4
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C
8
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D
7
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Solution
The correct option is D7 Let the natural number be x
As per given conditions, we get x−2x=477⇒x2−2x=477⇒7x2−14=47x⇒7x2−47x−14=0⇒7x2−49x+2x−14=0⇒7x(x−7)+2(x−7)=0⇒(7x+2)(x−7)=0⇒x=−27,7∴x=7(∵x∈N)