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Problem
Problem
The roots of the equation
x
2
−
6
x
+
7
=
0
x^2 - 6x + 7 = 0
x
2
−
6
x
+
7
=
0
are
α
\alpha
α
and
β
\beta
β
. Find a quadratic equation with roots
α
+
1
β
\alpha + \frac{1}{\beta}
α
+
β
1
and
β
+
1
α
\beta + \frac{1}{\alpha}
β
+
α
1
.
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