Two point charges $q_1 =+2C$ and $q_2 =-1C$ are separated by a distance $d$. The position on the line joining the two charges where a third charge $q = + 1C$ will be in equilibrium is at a distance

$d/\sqrt{2}-1$ from $q_2$ away $q_1$

Let electric field is zero at a distane x from q₂ charge away from q₁.

$\frac{K.q_2q}{4\pi \epsilon_0 x^2} = \frac{K q_1q}{4\pi \epsilon_0 (x+d)^2}$

$\Rightarrow (x+d)^2 = 2 x^2$

$\Rightarrow (x+d) = \pm \sqrt2 x$

$\Rightarrow x = \frac{d}{\sqrt2 -1} $