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1968 Swedish Mathematical Competition
1
1
Part of
1968 Swedish Mathematical Competition
Problems
(1)
min, max of x^2 + 2y^2 + 3z^2 when x^2 + y^2 + z^2 = 1
Source: 1968 Swedish Mathematical Competition p1
3/21/2021
Find the maximum and minimum values of
x
2
+
2
y
2
+
3
z
2
x^2 + 2y^2 + 3z^2
x
2
+
2
y
2
+
3
z
2
for real
x
,
y
,
z
x, y, z
x
,
y
,
z
satisfying
x
2
+
y
2
+
z
2
=
1
x^2 + y^2 + z^2 = 1
x
2
+
y
2
+
z
2
=
1
.
algebra
min
max
inequalities