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Korea Junior Mathematics Olympiad
2014 Korea Junior Math Olympiad
6
max of x^p+y^p+z^p when (x-1)^2 +(y-1)^2+(z-1)^2 = 27, p= 1+1/2+...+1/2^5
max of x^p+y^p+z^p when (x-1)^2 +(y-1)^2+(z-1)^2 = 27, p= 1+1/2+...+1/2^5
Source: KJMO 2014 p6
May 2, 2019
maximum
algebra
inequalities
Problem Statement
Let
p
=
1
+
1
2
+
1
2
2
+
1
2
3
+
1
2
4
+
1
2
5
.
p = 1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+\frac{1}{2^4}+\frac{1}{2^5}.
p
=
1
+
2
1
+
2
2
1
+
2
3
1
+
2
4
1
+
2
5
1
.
For nonnegative reals
x
,
y
,
z
x, y,z
x
,
y
,
z
satisfying
(
x
−
1
)
2
+
(
y
−
1
)
2
+
(
z
−
1
)
2
=
27
,
(x-1)^2 + (y-1)^2 + (z-1)^2 = 27,
(
x
−
1
)
2
+
(
y
−
1
)
2
+
(
z
−
1
)
2
=
27
,
find the maximum value of
x
p
+
y
p
+
z
p
.
x^p + y^p + z^p.
x
p
+
y
p
+
z
p
.
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