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Problems
Contests
National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2007 Hanoi Open Mathematics Competitions
10
10
Part of
2007 Hanoi Open Mathematics Competitions
Problems
(2)
HOMC (Vietnam)
Source:
1/25/2016
Let a; b; c be positive real numbers such that
1
b
c
+
1
c
a
+
1
a
b
≥
1
\frac{1}{bc}+\frac{1}{ca}+\frac{1}{ab} \geq 1
b
c
1
+
c
a
1
+
ab
1
≥
1
. Prove that
a
b
c
+
b
c
a
+
c
a
b
≥
1
\frac{a}{bc}+\frac{b}{ca}+\frac{c}{ab} \geq 1
b
c
a
+
c
a
b
+
ab
c
≥
1
.
algebra
smallest possible value of x^2+2y^2-x-2y-xy (HOMC 2007 Q10)
Source:
7/23/2019
What is the smallest possible value of
x
2
+
2
y
2
−
x
−
2
y
−
x
y
x^2+2y^2-x-2y-xy
x
2
+
2
y
2
−
x
−
2
y
−
x
y
?
algebra
minimum
inequalities