Let α\alphaα be a solution of x2+x+1=0x^2 + x + 1 = 0x2+x+1=0, and for some aaa and bbb in R\mathbb{R}R, [11613−1−12−2−14−8][4ab]=[000]. \begin{bmatrix} 1 & 16 & 13 \\-1 & -1 & 2 \\-2 & -14 & -8 \end{bmatrix} \begin{bmatrix} 4 \\a \\b \end{bmatrix} = \begin{bmatrix} 0 \\0 \\0 \end{bmatrix}. 1−1−216−1−14132−84ab=000. If 4α4+mαa+nαb=3\frac{4}{\alpha^4} + \frac{m} {\alpha^a} + \frac{n}{\alpha^b} = 3α44+αam+αbn=3, then m+nm + nm+n is equal to _____.
If the set of all values of a a a, for which the equation 5x3−15x−a=0 5x^3 - 15x - a = 0 5x3−15x−a=0 has three distinct real roots, is the interval (α,β) (\alpha, \beta) (α,β), then β−2α \beta - 2\alpha β−2α is equal to