If α,β  are the roots of the equation x2−(1+n2)x+12(1+n2+n4) , then α2+β2=

The given equation x2−(1+n2)x+12(1+n2+n4) α,β  are the roots of the equationSum of the roots: α+β=1+n2 Product of the roots: α×β=12(1+n2+n4) α2+β2=(α+β)2−2αβ =(1+n2)2−12×2(1+n2+n4) =1+n4+2n2−1−n2−n4 =n2