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Jozsef Wildt International Math Competition
2019 Jozsef Wildt International Math Competition
W. 2
Prove this inequality
Prove this inequality
Source: 2019 Jozsef Wildt International Math Competition-W. 2
April 30, 2020
inequalities
Problem Statement
If
0
<
a
≤
c
≤
b
0<a\leq c\leq b
0
<
a
≤
c
≤
b
then
(
b
30
−
a
30
)
(
b
30
−
c
30
)
36
b
10
≤
(
b
25
−
a
25
)
(
b
25
−
c
25
)
25
≤
(
b
30
−
a
30
)
(
b
30
−
c
30
)
36
(
a
c
)
10
\frac{(b^{30}-a^{30})(b^{30}-c^{30})}{36b^{10}}\leq \frac{(b^{25}-a^{25})(b^{25}-c^{25})}{25}\leq \frac{(b^{30}-a^{30})(b^{30}-c^{30})}{36(ac)^{10}}
36
b
10
(
b
30
−
a
30
)
(
b
30
−
c
30
)
≤
25
(
b
25
−
a
25
)
(
b
25
−
c
25
)
≤
36
(
a
c
)
10
(
b
30
−
a
30
)
(
b
30
−
c
30
)
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