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Kvant 2021
M2642
M2642
Part of
Kvant 2021
Problems
(1)
Weird inequality
Source: Kvant Magazine No. 3 2021 M2642
3/9/2023
The nonzero numbers
x
x{}
x
and
y
y{}
y
satisfy the inequalities
x
2
n
−
y
2
n
>
x
x^{2n}-y^{2n}>x
x
2
n
−
y
2
n
>
x
and
y
2
n
−
x
2
n
>
y
y^{2n}-x^{2n}>y
y
2
n
−
x
2
n
>
y
for some natural number
n
n{}
n
. Can the product
x
y
xy
x
y
be a negative number?Proposed by N. Agakhanov
algebra
inequalities
Kvant