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1998 Chile National Olympiad
4
x^{3/2} + 6x^{5/4} + 8x^{3/4}\ge 15x (Chile NMO 1998 P4)
x^{3/2} + 6x^{5/4} + 8x^{3/4}\ge 15x (Chile NMO 1998 P4)
Source:
November 24, 2021
algebra
inequalities
Problem Statement
a) Prove that for any nonnegative real
x
x
x
, holds
x
3
2
+
6
x
5
4
+
8
x
3
4
≥
15
x
.
x^{\frac32} + 6x^{\frac54} + 8x^{\frac34}\ge 15x.
x
2
3
+
6
x
4
5
+
8
x
4
3
≥
15
x
.
b) Determine all x for which the equality holds
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