Sub-topic 1
2026 · National One-Eighth
Free
$m^2+\dfrac{1}{m^2}$ from $m+\dfrac{1}{m}=7$
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Sub-topic 2
2026 · National Preliminary
Premium
$x^2+\dfrac{1}{x^2}$ and $x^4+\dfrac{1}{x^4}$ from $x-\dfrac{1}{x}=5$
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Sub-topic 3
2023 · National Preliminary
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$x^2+\dfrac{1}{x^2}$ from $x+\dfrac{1}{x}=5$ or $x-\dfrac{1}{x}=-7$
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Sub-topic 4
2026 · National Preliminary
Premium
$\dfrac{a^2}{b^2}+\dfrac{b^2}{a^2}$ from $\dfrac{a}{b}\pm\dfrac{b}{a}$
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Sub-topic 180
2023 · National Preliminary
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$x^2+\dfrac{1}{x^2}$ given $x+\dfrac{1}{x}=5$
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Sub-topic 181
2023 · National Preliminary
Premium
$x^2+\dfrac{1}{x^2}$ given $x-\dfrac{1}{x}=-7$
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Sub-topic 182
2023 · National Preliminary
Premium
$x^2+\dfrac{1}{x^2}$ given $x+\dfrac{1}{x}=-11$
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