Question

1. The sum of (x + 3) observations is (x4 -81). Find the mean of the observations. ​

Answer 1

Answer:

Question :-

The sum of (x + 3) observations is (x⁴-81). Find the mean of the observations.

$\boxed{\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}}$

Step-by-step explanation:

$\text{Mean \( \displaystyle =\frac{\text { Sum of observations }}{\text { Number of observations }} \)}$

$\begin{array}{l} \displaystyle\rm =\frac{x^{4}-81}{x+3} \\ \\ \displaystyle\rm=\frac{\left(x^{2}\right)^{2}-9^{2}}{x+3} \\ \\ \displaystyle\rm=\frac{\left(x^{2}-9\right)\left(x^{2}+9\right)}{x+3} \end{array}$

$\begin{array}{l} \displaystyle\rm =\frac{\left(x^{2}-3^{2}\right)\left(x^{2}+9\right)}{(x+3)} \\ \\ \displaystyle\rm=\frac{(x-3)(x+3)\left(x^{2}+9\right)}{(x+3)} \\ \\ \boxed{\color{green} \displaystyle\rm=(x-3)\left(x^{2}+9\right)} \end{array}$

Answer 2

Step-by-step explanation:

Answer:

Question :-

The sum of (x + 3) observations is (x⁴-81). Find the mean of the observations.

$\boxed{\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}}$

Step-by-step explanation:

$\text{Mean \( \displaystyle =\frac{\text { Sum of observations }}{\text { Number of observations }} \)}$

$\begin{gathered} \begin{array}{l} \displaystyle\rm =\frac{x^{4}-81}{x+3} \\ \\ \displaystyle\rm=\frac{\left(x^{2}\right)^{2}-9^{2}}{x+3} \\ \\ \displaystyle\rm=\frac{\left(x^{2}-9\right)\left(x^{2}+9\right)}{x+3} \end{array}\end{gathered}$

$\begin{gathered} \begin{array}{l} \displaystyle\rm =\frac{\left(x^{2}-3^{2}\right)\left(x^{2}+9\right)}{(x+3)} \\ \\ \displaystyle\rm=\frac{(x-3)(x+3)\left(x^{2}+9\right)}{(x+3)} \\ \\ \boxed{\color{green} \displaystyle\rm=(x-3)\left(x^{2}+9\right)} \end{array}\end{gathered}$