With reference to a number greater than one, the difference between itself and its reciprocal is 25% of the sum of itself and its reciprocal. By how much percent is the fourth power of the number greater than its square?
Answer & explanation
Correct answer: option 4
Let the no. = x
x - \(\frac{1}{×}\) = \(\frac{25}{100}\) (x + (\(\frac{1}{×}\))
x2 - 1 = \(\frac{1}{4}\) (x2 + 1 )
4x2 - 4 = x2 + 1
3x2 = 5
⇒ x2 = \(\frac{5}{3}\) & x4 = \(\frac{25}{9}\)
Required percentage = \(\frac{\frac{25}{9} -\frac{5}{3}}{\frac{5}{3}}\) × 100 = 66.7%