If α>β  and α,β are the roots of x2−5x+1=0  then α2−β2 =

The given equation is x2−5x+1=0 α,β  are the given roots and α>β Sum of the  roots : α+β=5,     Product of the roots :αβ=1      α2−β2=((α+β)(α−β))    α−β=(α+β)2−4αβ   (∵(α−β)2=(α+β)2−4αβ)                 = 25−4              = 21 ∴α2−β2 =5×21=521