Question

The sum of (x + 5) observations is x⁴ – 625. Find the mean of the observations.

Answer 1

We have, the sum of (x + 5) observations = x⁴ – 625

We know that, the mean of the n observations x₁, x₂, ... x_n is given by `(x_1 + x_2 + ...  x_n)/n`.

∴ The mean of (x + 5) observations

= `("Sum of"  (x + 5)  "observations")/(x + 5)`

= `(x^4 - 625)/(x + 5)`

= `((x^2)^2 - (25)^2)/(x + 5)`

= `((x^2 + 25)(x^2 - 25))/(x + 5)`  ...[∵ a² – b² = (a + b)(a – b)]

= `((x^2 + 25)[(x)^2 - (5)^2])/(x + 5)`

= `((x^2 + 25)(x + 5)(x - 5))/((x + 5))`

= (x² + 25)(x – 5)