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Byju's Answer
Standard XII
Mathematics
Absolute Value Function
Prove that:a+...
Question
Prove that :
a
+
b
+
2
c
a
b
c
b
+
c
+
2
a
b
c
a
c
+
a
+
2
b
=
2
a
+
b
+
c
3
Open in App
Solution
Let
LHS
=
Δ
=
a
+
b
+
2
c
a
b
c
b
+
c
+
2
a
b
c
a
c
+
a
+
2
b
⇒
∆
=
2
a
+
2
b
+
2
c
a
b
2
a
+
2
b
+
2
c
b
+
c
+
2
a
b
2
a
+
2
b
+
2
c
a
c
+
a
+
2
b
Applying
C
1
→
C
1
+
C
2
+
C
3
=
2
a
+
b
+
c
1
a
b
1
b
+
c
+
2
a
b
1
a
c
+
a
+
2
b
Taking
out
2
(
a
+
b
+
c
)
common
from
C
1
∆
=
2
a
+
b
+
c
1
a
b
0
b
+
c
+
a
0
0
-
b
-
c
-
a
c
+
a
+
b
Applying
R
2
→
R
2
-
R
1
and
R
2
→
R
2
-
R
3
=
2
a
+
b
+
c
a
+
b
+
c
a
+
b
+
c
1
a
b
0
1
0
0
-
1
1
Taking
out
(
a
+
b
+
c
)
common
from
R
2
and
R
3
=
2
a
+
b
+
c
3
1
1
-
0
Expanding
along
C
1
=
2
a
+
b
+
c
3
=
RHS
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0
Similar questions
Q.
Prove the following :
∣
∣ ∣
∣
a
+
b
+
2
c
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b
c
b
+
c
+
2
a
b
c
a
c
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a
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b
∣
∣ ∣
∣
=
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3
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Prove the following identities :
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Q.
Prove the following using properties of determinants:
∣
∣ ∣
∣
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b
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2
c
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b
c
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+
c
+
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a
b
c
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+
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)
3
Q.
Show that
∣
∣ ∣
∣
a
+
b
+
2
c
a
b
c
b
+
c
+
2
a
b
c
a
c
+
a
+
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b
∣
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∣
=
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a
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3
Q.
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