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Byju's Answer
Standard XII
Mathematics
Evaluation of a Determinant
Q. Prove that...
Question
Q. Prove that:
x
3
+
y
3
+
z
3
-
3
x
y
z
=
x
+
y
+
z
x
2
+
y
2
+
z
2
-
x
y
-
y
z
-
z
x
Open in App
Solution
Dear student,
T
a
k
i
n
g
R
.
H
.
S
(
x
+
y
+
z
)
x
2
+
y
2
+
z
2
-
x
y
-
y
z
-
z
x
=
x
x
2
+
y
2
+
z
2
-
x
y
-
y
z
-
z
x
+
y
x
2
+
y
2
+
z
2
-
x
y
-
y
z
-
z
x
+
z
x
2
+
y
2
+
z
2
-
x
y
-
y
z
-
z
x
=
x
3
+
x
y
2
+
x
z
2
-
x
2
y
-
x
y
z
-
z
x
2
+
x
2
y
+
y
3
+
y
z
2
-
x
y
2
-
y
2
z
-
x
y
z
+
z
x
2
+
z
y
2
+
z
3
-
x
y
z
-
y
z
2
-
z
2
x
=
x
3
+
y
3
+
z
3
-
3
x
y
z
=
L
.
H
.
S
H
e
n
c
e
p
r
o
v
e
d
Regards
Suggest Corrections
2
Similar questions
Q.
Using the identity and proof:
x
3
+
y
3
+
z
3
−
3
x
y
z
=
(
x
+
y
+
z
)
(
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
)
.
Q.
x
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+
y
3
+
z
3
−
3
x
y
z
≥
(
x
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y
+
z
)
(
x
2
+
y
2
+
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2
−
x
y
−
y
z
−
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x
)
.
State whether the above statement is true or false.
Q.
If
x
+
y
+
z
=
6
and
x
y
+
y
z
+
z
x
=
12
then show that
x
3
+
y
3
+
z
3
=
3
x
y
z
Q.
Prove that:
x
3
+
y
3
+
z
3
−
3
x
y
z
=
1
2
(
x
+
y
+
z
)
[
(
x
−
y
)
2
+
(
y
−
z
)
2
+
(
z
−
x
)
2
]
Q.
x
3
+
y
3
+
z
3
−
3
x
y
z
a
3
+
b
3
+
c
3
−
3
a
b
c
×
a
2
+
b
2
+
c
2
−
a
b
−
b
c
−
c
a
x
2
+
y
2
+
z
2
−
x
y
−
y
z
−
z
x
equals
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