Question

The sum of four observations is $p^2+31p$. If the mean of these observations is $8$, find the value of $p$, where $p$ be any positive integer.

Answer 1

Given the sum of four observations is $p^2+31p$. of the mean of these observations is 8.

Sum of four observations is $p^2+31p$

$\therefore$ mean = \dfrac{Sum \, of \ observations}{No \ of \ observations}$

$8=\frac{p^2+31p}{4}$

$32=p^2+31p$

$p^2+31p-32=0$

Here spiting the $31p$ as $32p-p$

$p^2+32p-p-32=0$

$p(p+32)-1(p+32)=0$

$(p+32)(p-1)=0$

$p+32=0$ & $p-1=0$

$p=-32$ & $p=1$

we are given p be any positive integer then value of p is $1$.