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TS EAMCET 20-July-2022 Shift 2 Solved Paper
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© examsnet.com
Question : 8
Total: 160
If
α
,
β
are the roots of the equation
x
2
−
2
x
+
2
=
0
then
α
2020
+
β
2020
=
2
1011
−
2
1011
2
2021
2
−
2021
Validate
Solution:
x
2
−
2
x
+
2
=
0
⇒
x
2
−
2
x
+
1
=
−
1
⇒
(
x
−
1
)
2
=
−
1
⇒
x
−
1
=
±
√
−
1
⇒
x
=
1
+
√
−
1
⇒
x
=
1
±
i
Taking
α
=
1
+
i
,
β
=
1
−
i
α
2
=
(
1
+
i
)
2
=
1
+
(
i
)
2
+
2
i
=
1
−
1
+
2
i
=
2
i
β
2
=
(
1
−
i
)
2
=
1
+
(
i
)
2
−
2
i
=
1
−
1
−
2
i
=
−
2
i
Now,
α
2020
+
β
2020
=
(
α
2
)
1010
+
(
β
2
)
1010
=
(
2
i
)
1010
+
(
−
2
i
)
1010
=
2
1010
[
i
1010
+
(
−
i
)
1010
]
=
2
1010
[
2
(
i
1010
)
]
=
2
1011
(
i
)
2
=
2
1011
(
−
1
)
=
−
2
1011
© examsnet.com
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