If x(i+j+k) is a unit vector then value of x is :

$x(\hat{i}+\hat{j}+\hat{k}) = \vec{y}$

so $|\vec{y}| = 1$

⇒ $\sqrt{x^2+x^2+x^2} = 1$

so $\sqrt{3 x^2} = 1$

so $x = ±\frac{1}{\sqrt{3}}$