If $$a,\,b$$ and $$c$$ are distinct positive numbers, then the expression
$$\left( {b + c - a} \right)\left( {c + a - b} \right)\left( {a + b - c} \right) - abc$$ is

For $$a \le 0,$$ determine all real roots of the equation $$${x^2} - 2a\left| {x - a} \right| - 3{a^2} = 0$$$

If the quadratic equations $${x^2} + ax + b = 0$$ and $${x^2} + bx + a = 0$$ $$(a \ne b)$$ have a common root, then the numerical value of a + b is..........................

The solution of equation $${\log _7}\,{\log _5}\,\left( {\sqrt {x + 5} + \sqrt x } \right) = 0$$ is ........................