If αand βare the roots of the equationsx2-(1+n2)x+12(1+n2+n4)=0, then α2+β2is equal to
n2
-n2
n4
-n4
Find the value of α2+β2:
Given that αand βare the roots of the equationsx2-(1+n2)x+12(1+n2+n4)=0,
⇒(α+β)=1+n2;(αβ)=(1+n2+n4)2
Now,
⇒(α2+β2)=(1+n2)2–2×12(1+n2+n4)⇒(α2+β2)=1+n4+2n2–1–n2–n4⇒(α2+β2)=n2 (α2+β2)=(α+β)2–2αβ
Hence, the correct option is (A).