Question

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 per-
centage (correct one decimal
place) is the fourth power of the
number greater than its square?​

Answer 1

Answer:

Let the number be x.

According to the question:

X - 1/x = 25/100 x (x + 1/x)

x² - 1 = ¹4 (x² + 1)

4x² - 4 = x² + 1

3x² = 5

x² = 5/3

→ x4 = 25/9

:: Required percentage = 25/9- 5/3x 100 = 66.7%

Hope this helps you...