Prove that the difference of a number and its reciprocal will be alway

1.	Prove that the difference of a number and its reciprocal will be always positive.
Answer» Number = x, its reciprocal = 1/x then, x − \(\frac{1}{x}\) = k \(x^2-kx-1=0,x=\frac{+k\,\pm \sqrt{k^2+\,4} }{2}\) Since k being a positive number, k² + 4 also negative.

Prove that the difference of a number and its reciprocal will be always positive.

Answer»

Number = x, its reciprocal = 1/x then, x − \(\frac{1}{x}\) = k

\(x^2-kx-1=0,x=\frac{+k\,\pm \sqrt{k^2+\,4} }{2}\)

Since k being a positive number, k² + 4 also negative.

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Prove that the difference of a number and its reciprocal will be always positive.

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