Question

Let ' $p$ ' be the greatest integer for which $5m^2-16,2pm,p^2$ are distinct consecutive terms of an A.P. where $m\in R$. If common difference of the A.P. is $\left(\frac{A}{B}\right),A,B\in N$ then find the least value of $(26B-A)$

Answer 1

Answer: 2

$5m^2-16+p^2=4pm$
$5m^2-4pm+p^2-16=0$
$D\ge 0p\in [-\sqrt{80},\sqrt{80}]$
$\therefore$ Greatest integral value of ' $p$ ' is 8 .

$5m^2-16,2pm,p^2$
$\Rightarrow \frac{64}{5},\frac{192}{5},\frac{320}{5}$
$\therefore \text{ Common difference }=\frac{128}{5}$