Three identical spheres each of mass M are placed at the corners of...

The diagram represents the locations of the masses as mentioned in the question.

For point $1$, \overset{\to}{{r}_{1}} = 0\overset{^}{i} + 0\overset{^}{j} for point $2$, \overset{\to}{{r}_{2}} = 3\overset{^}{i} + 0\overset{^}{j} and for point $3$, \overset{\to}{{r}_{3}} = 0\overset{^}{i} + 3\overset{^}{j}.

The formula for centre of mass is

$\overset{\to}{r}com = \dfrac{{m}_{1}\overset{\to}{{r}_{1}} + {m}_{2}\overset{\to}{{r}_{2}} + {m}_{3}\overset{\to}{{r}_{3}}}{{m}_{1} + {m}_{2} + {m}_{3}}$

⇒ \overset{\to}{r}com = \dfrac{M\left(0\overset{^}{i} + 0\overset{^}{j}\right) + M\left(3\overset{^}{i}\right) + M\left(3\overset{^}{j}\right)}{3M}

⇒ \overset{\to}{r}com = \overset{^}{i} + \overset{^}{j}

\left|\overset{\to}{r}com\right| = \sqrt{{1}^{2} + {1}^{2}} = \sqrt{2} = \sqrt{x}$</p><p>$⇒ x = 2