If α and β be the roots of the equation x2+px−12p2=0, where p∈R. Then the minimum value of α4+β4 is
22
2-2
2
2+2
Here,
α4+β4=α2+β22−2α2β2=(α+β)2−2αβ2−2(αβ)2=p2+1p22−12p4=p4+12p4+2=p2−12p22+2+2≥2+2
Thus, the minimum value of α4+β4 is 2+2