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Byju's Answer
Standard XII
Mathematics
Arithmetic Progression
If logxy, l...
Question
If
l
o
g
x
y
,
l
o
g
z
x
,
l
o
g
y
z
are in G.P.,
x
y
z
=
64
and
x
3
,
y
3
,
z
3
are in A.P., find
x
+
y
+
z
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Solution
According to question,
l
o
g
z
x
l
o
g
x
y
=
l
o
g
y
z
l
o
g
z
x
⇒
(
l
o
g
x
)
3
=
(
l
o
g
z
)
3
⇒
x
=
z
Since
2
y
3
=
x
3
+
z
3
⇒
x
2
=
y
3
or
x
=
y
Given
x
y
z
=
64
&
x
=
y
=
z
∴
x
=
y
=
z
=
4
&
x
+
y
+
z
=
12
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Similar questions
Q.
Given
x
3
,
y
3
,
z
3
are in
A
.
P
.
and
l
o
g
x
y
,
l
o
g
z
x
,
l
o
g
y
z
are in
G
.
P
.
If
x
y
z
=
64
, then prove that
x
=
y
=
z
=
4
.
Q.
1
l
o
g
x
y
x
y
z
+
1
l
o
g
y
z
x
y
z
+
1
l
o
g
z
x
x
y
z
=
Q.
If
x
+
y
+
z
=
0
and
x
3
+
y
3
x
y
z
=
y
3
+
z
3
x
y
z
=
x
3
+
z
3
x
y
z
=
a
, then which of the following can be a?
Q.
If
x
=
√
2
−
1
,
y
=
1
−
√
3
and
z
=
√
3
−
√
2
, find
x
3
+
y
3
+
z
3
−
x
y
z
.
Q.
If
x
+
y
+
z
=
1
,
x
y
+
y
z
+
z
x
=
−
1
&
x
y
z
=
−
1
, find
x
3
+
y
3
+
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3
.
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