alpha/bita^2+bita/alpha^2
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Step-by-step explanation:
α
2
,−β
2
are the roots of a
2
x
2
+x+1−a
2
=0
⇒α
2
−β
2
=−
a
2
1
,
And
⇒α
2
(−β
2
)=
a
2
1−a
2
(α
2
+β
2
)
2
=(α
2
−β
2
)
2
+4α
2
β
2
=
a
4
1
+4(
a
2
a
2
−1
)=
a
4
1
+4−
a
2
4
=(2−
a
2
1
)
2
⇒α
2
+β
2
=2−
a
2
1
β
2
=
2
1
[(α
2
+β
2
)−(α
2
−β
2
)]
=
2
1
[2−
a
2
1
+
a
2
1
]=1
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