Question

consider the equation an^2= 182 where a is any number between 2 and 5 and n is a positive integer.What are the possible values of n

Answer 1

$Given \: equation \: an^{2} = 182 \: and$

$where\: 'a' \:is \:any\: number\: between\: 2$

$and \:5\: and\: n\: is \:a\: positive \: integer$

$an^{2} = 182 ,\:and \: a = 3 \:and 4$

$\implies n^{2} = \frac{182}{a} \: --(1)$

$i ) If \: a = 3 \: then \: n^{2} = \frac{182}{3}$

$\implies n = \pm \sqrt{\frac{182}{3}} \: \blue{ \cancel { \in} Z}$

$ii) If \: a = 4 \: then \: n^{2} = \frac{182}{4}$

$\implies n = \pm \sqrt{\frac{91}{2}} \: \blue{ \cancel { \in} Z}$

Therefore.,

$\red{ Possible \:values \:of \: n } \green { = \{ \} }$

•••♪