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India Contests
Regional Mathematical Olympiad
2015 India Regional MathematicaI Olympiad
7
7
Part of
2015 India Regional MathematicaI Olympiad
Problems
(1)
(1+x)(1+y)(1+z)<=4(1+xyz) with a condition on reals x,y,z
Source: RMO (Mumbai Region) 2015 P7
12/6/2015
Let
x
,
y
,
z
x,y,z
x
,
y
,
z
be real numbers such that
x
2
+
y
2
+
z
2
−
2
x
y
z
=
1
x^2+y^2+z^2-2xyz=1
x
2
+
y
2
+
z
2
−
2
x
yz
=
1
. Prove that
(
1
+
x
)
(
1
+
y
)
(
1
+
z
)
≤
4
+
4
x
y
z
.
(1+x)(1+y)(1+z)\le 4+4xyz.
(
1
+
x
)
(
1
+
y
)
(
1
+
z
)
≤
4
+
4
x
yz
.
inequalities
inequalities proposed
trig identities
trigonometric substitution