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8.1
a^2b^2(a^2b^2+4)=2(a^6+b^6) - All-Russian MO 2000 Regional (R4) 8.1
a^2b^2(a^2b^2+4)=2(a^6+b^6) - All-Russian MO 2000 Regional (R4) 8.1
Source:
September 25, 2024
algebra
irrational
Problem Statement
Non-zero numbers
a
a
a
and
b
b
b
satisfy the equality
a
2
b
2
(
a
2
b
2
+
4
)
=
2
(
a
6
+
b
6
)
.
a^2b^2(a^2b^2 + 4) = 2(a^6 + b^6).
a
2
b
2
(
a
2
b
2
+
4
)
=
2
(
a
6
+
b
6
)
.
Prove that at least one of them is irrational.
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