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Byju's Answer
Standard XII
Mathematics
Theorems for Differentiability
If a, b, c ar...
Question
If a, b, c are three positive real number then show :
a
b
+
c
+
b
a
+
c
+
c
a
+
b
≥
3
2
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Solution
a
b
+
c
+
b
a
+
c
+
c
a
+
b
3
≥
3
b
+
c
a
+
a
+
c
b
+
a
+
b
c
(
A
M
>
H
M
)
a
b
+
c
+
b
a
+
c
+
c
a
+
b
3
≥
3
b
a
+
a
b
+
c
a
+
a
c
+
c
b
+
b
c
a
b
+
c
+
b
a
+
c
+
c
a
+
b
3
≥
3
6
(
∵
a
b
+
b
a
≥
2
)
(
A
M
>
G
M
)
a
b
+
c
+
b
a
+
c
+
c
a
+
b
≥
3
2
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Q.
If a, b, c are three distinvt positive real numbers which are in H.P., then
3
a
+
2
b
2
a
−
b
+
3
c
+
2
b
2
c
−
b
is