D=(sin2θ)2−4(1−2sin22θ)(1−43sin22θ)=(sin2θ)2−4(1−45sin22θ+83sin42θ)D=−23sin42θ+6sin22θ−4>03sin42θ−12sin22θ+8<0sin22θ=612±122−12.8=612±43=36±23sin22θ=2±32, but sin22θ∈[0,1]∴α=2−32,β=1→(α−2)2=34,(β−1)2=03(α−2)2+(β−1)2=4
Let S={sin22θ:(sin4θ+cos4θ)x2+(sin2θ)x+(sin6θ+cos6θ)=0 has real roots }. If α and β be the smallest and largest elements of the set S, respectively, then 3((α−2)2+(β−1)2) equals _________
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