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Standard XII
Mathematics
Arithmetic Mean
Question
If
f
(
x
+
y
,
x
−
y
)
=
x
y
, then the arithmetic mean of
f
(
x
,
y
)
and
f
(
y
,
x
)
is
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Solution
Verified by Toppr
Given:
f
(
x
+
y
,
x
−
y
)
=
x
y
Replacing
x
by
x
+
y
2
and
y
by
x
−
y
2
Gives
f
(
x
,
y
)
=
x
2
−
y
2
4
Now the arithmetic mean is
f
(
x
,
y
)
+
f
(
y
,
x
)
2
=
x
2
−
y
2
4
+
y
2
−
x
2
4
2
=
0
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