Six X' s have to be placed in the squares of figure below in such a way that each row contains at least one X. In how many different ways can this be done.

Solve for $$x:{4^x} - {3^{^{x - {1 \over 2}}}}\, = {3^{^{x + {1 \over 2}}}}\, - {2^{2x - 1}}$$

Sketch the solution set of the following system of inequalities: $$${x^2} + {y^2} - 2x \ge 0;\,\,3x - y - 12 \le 0;\,\,y - x \le 0;\,\,y \ge 0.$$$

Solve for $$x:\,\sqrt {x + 1} - \sqrt {x - 1} = 1.$$