Question

For what values of x, the number $-\frac{2}{7}x,x,-\frac{7}{2}$ are in G.P?

Answer 1

Given $\frac{-2}{7}x,x,\frac{-7}{2}$ are is G.P for a, b, c in A.P $b^2=ac$

$\therefore x^2=\frac{-2}{7}x\times \frac{-7}{2}$

$x^2-x=0$

$x(x-1)=0$

$\Rightarrow x=1$

$\therefore$ for $x=1$.

The numbers are in G.P.