Question

If $-\frac{2}{7},m,-\frac{7}{2}(m+2)$ are in G.P., find the values of $m$.

Answer 1

$\frac{m}{(-\frac{2}{7})}=\frac{\frac{-7(m+2)}{2}}{m}$

$\Rightarrow \frac{-7m}{2}=\frac{-7m-14}{2m}$

$\Rightarrow -7m^2=-(7m+14)$

$\Rightarrow m^2=m+2$ by dividing the complete equation by $-7x$

$\Rightarrow m^2-m-2=0$

$\Rightarrow m^2-2m+m-2=0$

$\Rightarrow m(m-2)+(m-2)=0$

$\Rightarrow (m-2)(m+1)=0$
$\therefore m=-1,m=2$