1.
Let α,β\alpha, \beta (α<β\alpha < \beta) be the values of mm for which the equations
x+y+z=1x + y + z = 1

x+2y+4z=mx + 2y + 4z = m

x+4y+10z=m2x + 4y + 10z = m^2

have infinitely many solutions. Then the value of (α2+β3)(\alpha^2 + \beta^3) is equal to: