Question

With reference to a number greater than one, the difference between itself and it's reciprocal is 25% of the sum of itself and it's reciprocal.by howmuch percentage(correct one decimal place)is the fourth power of the number greater than it's square ​

Answer 1

Answer:

Step-by-step explanation:

Let say number = N

then reciprocal = 1/N

N - 1/N  = 25 % of ( N + 1/N)

=> (N - 1/N) = (1/4)(N + 1/N)

=> 4N - 4/N = N + 1/N

=> 3N = 5/N

=> N² = 5/3

=> N = √(5/3)

N⁴ = (N²)² = (5/3)² = 25/9

N² = 5/3

N⁴ - N²  = 25/9 - 5/3  = 10/9

%  = (10/9)/(5/3)  * 100

= 200/3 %

= 66.67 %