Let $$x_1, x_2, x_3, x_4$$ be the solution of the equation $$4 x^4+8 x^3-17 x^2-12 x+9=0$$ and $$\left(4+x_1^2\right)\left(4+x_2^2\right)\left(4+x_3^2\right)\left(4+x_4^2\right)=\frac{125}{16} m$$. Then the value of $$m$$ is _________.

The number of real solutions of the equation $$x|x+5|+2|x+7|-2=0$$ is __________.

The number of distinct real roots of the equation $$|x||x+2|-5|x+1|-1=0$$ is __________.

Let $$a, b, c$$ be the lengths of three sides of a triangle satistying the condition $$\left(a^2+b^2\right) x^2-2 b(a+c) x+\left(b^2+c^2\right)=0$$. If the set of all possible values of $$x$$ is the interval $$(\alpha, \beta)$$, then $$12\left(\alpha^2+\beta^2\right)$$ is equal to __________.