The equation $$x - {2 \over {x - 1}} = 1 - {2 \over {x - 1}}$$ has

If $$\,{a^2} + {b^2} + {c^2} = 1$$, then ab + bc + ca lies in the interval

The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x \right| + 2 = 0$$ is

The largest interval for which $${x^{12}} - {x^9} + {x^4} - x + 1 > 0$$ is