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MathNet 2026 — Part 03 Question 198

Math Olympiad Vault · MathNet 2026 — Part 03

Question 198

The non-null real numbers $a$ and $b$ check the equality $$
\frac{a^{2} b^{2}}{a^{4}-2 b^{4}}=1
$$ Find, reasonably, all the values taken by the expression $$
\frac{a^{2}-b^{2}}{a^{2}+b^{2}}
$$