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Byju's Answer
Standard XII
Mathematics
Sum of Infinite Terms of a GP
If a > 0, b...
Question
If
a
>
0
,
b
>
0
and
a
+
b
=
4
, find the maximum value of ab.
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Solution
given
a
+
b
=
4
,
a
>
0
,
b
>
0
We know that for a finite number of terms (real)
A.M
≥
G.M
Consider the terms to be
a
,
b
A.M
=
a
+
b
2
,
G.M
=
√
a
b
A.M
≥
G.M
a
+
b
2
≥
√
a
b
2
≥
√
a
b
a
b
≤
4
Maximum value of
a
b
is
4
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