If α≠βand α2=5α−3,β2=5β−3, then the equation having α/βand β/α as its roots, is

We haveα2=5α−3⇒α2−5α+3=0⇒α=5±132Similarly, β2=5β−3⇒β=5±132Since, α≠β∴ α=5+132 and β=5−132or, α=5−132 and β=5+132Thus, in either case, we obtainα2+β2=14(50+26)=19,and, αβ=14(25−13)=3, in both the cases.Thus, the equation having a/β  and β/ a as its roots isx2−xαβ+βα+αβαβ=0⇒ x2−xα2+β2αβ+1=0⇒3x2−19x+3=0