alpha and beta the root of x^2+mx+m^2-8=0 find alpha^2+(alpha*beta)+bata^2
using what you know about the sum and product of roots of a quadratic,
a+b = -m
ab = m^2-8
a^2+ab+b^2 = (a+b)^2-ab = m^2-(m^2-8) = 8
a+b = -m
ab = m^2-8
a^2+ab+b^2 = (a+b)^2-ab = m^2-(m^2-8) = 8