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AP EAMCET Engineering 2018 Apr 23 Shift 2 Paper
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© examsnet.com
Question : 9
Total: 160
If a,b,c are non zero real number with c ≠ 1 such that
a
2
+
b
2
+
c
2
=
c
and if
α
=
a
+
i
b
1
−
c
then
a
2
+
b
2
=
|
α
|
2
(
1
+
|
α
|
2
)
2
|
α
|
4
(
1
+
|
α
|
2
)
2
|
α
|
(
1
+
|
α
|
2
)
|
α
|
1
+
|
α
|
Validate
Solution:
Consider the expression,
α
=
a
+
i
b
1
−
c
|
α
|
2
=
a
2
+
b
2
(
1
−
c
)
2
...... (I)
And,
a
2
+
b
2
+
c
2
=
c
a
2
+
b
2
=
c
(
1
−
c
)
...... (II)
From equation (I) and (II),
|
α
|
2
=
c
1
−
c
=
1
+
|
α
|
2
1
=
1
1
−
c
1
−
c
=
1
1
+
|
α
|
2
...... (III)
From equation (I) and (III),
|
α
|
2
=
a
2
+
b
2
(
1
1
+
|
α
|
2
)
2
a
2
+
b
2
=
|
α
|
2
(
1
+
|
α
|
2
)
2
© examsnet.com
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