Given α2=5α−3 and β2=5β−3 hence, α and β satisfies x2=5x−3 x2−5x+3=0 .......(1) sum of roots α+β=−b∕a=5 product of roots α.β=c∕a=3 quadratic equation whose roots are
α
β
,
β
α
is given by x2−(
α
β
+
β
α
)x+(
α
β
×
β
α
)=0 ......(2) Now,
α
β
+
β
α
=
α2+β2
αβ
α
β
+
β
α
=
(α+β)2−2αβ
αβ
α
β
+
β
α
=
25−2×3
3
α
β
+
β
α
=
19
3
And
α
β
×
β
α
=1 On putting this value in equation (2), we get x2−(