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CAT 2023 Slot 1 Solved Paper
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© examsnet.com
Question : 64
Total: 66
For some positive and distinct real numbers
x
,
y
and
z
, if
frac
1
sqrt
y
+
sqrt
z
is the arithmetic mean of
frac
1
sqrt
x
+
sqrt
z
and
frac
1
sqrt
x
+
sqrt
y
, then the relationship which will always hold true, is
√
x
,
√
z
and
√
y
are in arithmetic progression
y
,
x
and
z
are in arithmetic progression
x
,
y
and
z
are in arithmetic progression
√
x
,
√
y
and
√
z
are in arithmetic progression
Validate
Solution:
Given that
1
√
y
+
√
z
is the arithmetic mean of
1
√
x
+
√
z
and
1
√
x
+
√
y
⇒
2
√
y
+
√
z
=
1
√
x
+
√
z
+
1
√
x
+
√
y
⇒
2
(
√
x
+
√
z
)
(
√
x
+
√
y
)
=
(
√
y
+
√
z
)
(
√
x
+
√
y
+
√
x
+
√
z
)
⇒
2
(
x
+
√
x
y
+
√
x
z
+
√
y
z
)
=
2
√
x
y
+
y
+
√
y
z
+
2
√
x
z
+
√
y
z
+
z
⇒
2
x
=
y
+
z
⇒
y
,
x
,
z
are in A.P. as
x
is the arithmetic mean of
y
and
z
.
© examsnet.com
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