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Problem
Problem
If
α
,
β
\alpha, \beta
α
,
β
are the roots of the equation
λ
(
x
2
−
x
)
+
x
+
5
=
0
\lambda(x^2 - x) + x + 5 = 0
λ
(
x
2
−
x
)
+
x
+
5
=
0
. If
λ
1
\lambda_1
λ
1
and
λ
2
\lambda_2
λ
2
are two values of
λ
\lambda
λ
for which the roots
α
,
β
\alpha, \beta
α
,
β
are related by
α
β
+
β
α
=
4
5
\frac{\alpha}{\beta} + \frac{\beta}{\alpha} = \frac{4}{5}
β
α
+
α
β
=
5
4
, find the value of
λ
1
λ
2
+
λ
2
λ
1
\frac{\lambda_1}{\lambda_2} + \frac{\lambda_2}{\lambda_1}
λ
2
λ
1
+
λ
1
λ
2
.
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