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 (4+x_1^2)(4+x_2^2)(4+x_3^2)(4+x_4^2)=125/16 m. Then the value…

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