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AP EAMCET Engineering 23 Apr 2019 Shift 1 Paper
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© examsnet.com
Question : 6
Total: 160
If x = α , y = β , z = γ is the solution, for the system of equations
2x - y + 8z = 13
3x + 4y + 5z = 18
5x - 2y + 7z = 20
then αβ + βγ + γα =
1
0
7
- 3
Validate
Solution:
By the Cramer’s rule,
x
=
α
=
Δ
1
Δ
y
=
β
=
Δ
2
Δ
z
=
γ
=
Δ
3
Δ
Where,
Δ
=
|
2
−
1
−
8
3
4
5
5
−
2
7
|
=
2
(
28
+
10
)
+
1
(
21
−
25
)
+
8
(
−
6
−
20
)
=
76
−
4
−
208
=
−
136
And,
Δ
1
=
|
13
−
1
−
8
18
4
5
20
−
2
7
|
=
13
(
28
+
10
)
+
1
(
126
−
100
)
+
8
(
−
36
−
80
)
=
494
+
26
−
928
=
−
408
And,
Δ
2
=
|
2
13
−
8
3
18
5
5
20
7
|
=
2
(
126
−
100
)
−
13
(
21
−
25
)
+
8
(
60
−
90
)
=
52
+
52
−
240
=
−
136
And,
Δ
3
=
|
2
−
1
13
3
4
18
5
−
2
20
|
=
2
(
80
+
36
)
+
1
(
60
−
90
)
+
13
(
−
6
−
20
)
=
232
−
30
−
338
=
−
136
So
,
α
=
3
,
β
=
1
,
γ
=
1
This implies,
α
β
+
β
γ
+
γ
α
=
3
+
1
+
3
= 7
© examsnet.com
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