If α≠β but α2=5α-3 and β2=5β-3, then the equation whose roots are α/β and β/α is
3x2-25x+3=0
x2+5x-3=0
x2-5x+3=0
3x2-19x+3=0
α2-5α+3=0 ...(i)
β2-5β+3=0 ...(ii)
From (i)-(ii),
⇒(α2-β2)-5α+5β=0
⇒α2-β2=5(α-β)⇒α+β=5
From (i)+(ii),
⇒(α2+β2)-5(α+β)+6=0
⇒(α2+β2)-5.5+6=0⇒α2+β2=19
Then (α+β)2=α2+β2+2αβ
⇒25=19+2αβ⇒αβ=3
then the equation, whose roots are αβ and βα is
x2-x(αβ+βα)+αβ.βα=0
⇒x2-x(α2+β2αβ)+1=0
⇒x2-x.193+1=0⇒3x2-19x+3=0