Construct the correlation matrix ((1,x,x),(1,x,1),(x,1,1)) = C. For any vector v, we need dot(v, dot(C,v)) >= 0. Choose v= (1,1,1) to get x >= -1/2. To get the upper bound of 1, compute det (C) to get 2x^3 -3x^2 +1 >= 0. We know x=-1/2 is a zero, and we have 2 more. We can easily check that 1 is a zero. Thus x in [-1/2, 1].

(-1/2, 1)