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National and Regional Contests
Sweden Contests
Swedish Mathematical Competition
1969 Swedish Mathematical Competition
4
4
Part of
1969 Swedish Mathematical Competition
Problems
(1)
min largest value of |y^2 - xy| for y in [0, 1]
Source: 1969 Swedish Mathematical Competition p4
3/21/2021
Define
g
(
x
)
g(x)
g
(
x
)
as the largest value of
∣
y
2
−
x
y
∣
|y^2 - xy|
∣
y
2
−
x
y
∣
for
y
y
y
in
[
0
,
1
]
[0, 1]
[
0
,
1
]
. Find the minimum value of
g
g
g
(for real
x
x
x
).
min
algebra
inequalities