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AP EAPCET 05-Jul-2022 Shift 1 Paper
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© examsnet.com
Question : 2
Total: 160
Let
f
:
R
−
{
−
1
2
}
→
R
be defined by
f
(
x
)
=
x
−
2
2
x
+
1
. If
α
,
β
satisfy the equation
f
(
f
(
x
)
)
=
−
x
, then
4
(
α
2
+
β
2
)
=
17
12
24
34
Validate
Solution:
👈: Video Solution
f
(
x
)
=
x
−
2
2
x
+
1
f
(
f
(
x
)
)
=
−
x
(Given)
⇒
f
(
x
)
−
2
2
(
f
(
x
)
)
+
1
=
−
x
x
−
2
2
x
+
1
−
2
⇒
2
x
−
4
2
x
+
1
+
1
⇒
x
−
2
−
4
x
−
2
2
x
−
4
+
2
x
+
1
=
−
x
⇒
−
3
x
−
4
4
x
−
3
=
−
x
⇒
3
x
+
4
4
x
−
3
=
x
⇒
3
x
+
4
=
4
x
2
−
3
x
⇒
4
x
2
−
6
x
−
4
=
0
⇒
2
x
2
−
3
x
−
2
=
0
Now,
(
α
+
β
)
2
=
α
2
+
β
2
+
2
α
β
⇒
9
4
=
α
2
+
β
2
−
2
[
∵
α
β
=
−
1
]
⇒
α
2
+
β
2
=
17
4
⇒
4
(
α
2
+
β
2
)
=
17
© examsnet.com
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