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Home » Let $ x = \frac5 + \sqrt212 $, then $ x + \frac1x = 5 $. Compute numerically: - Dachbleche24

Let $ x = \frac5 + \sqrt212 $, then $ x + \frac1x = 5 $. Compute numerically: - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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\frac{x^2}{100} + 1 - \frac{x^2}{64} = 1
x^2\left( \frac{1}{100} - \frac{1}{64} \right) = 0
x^2 \left( \frac{64 - 100}{6400} \right) = 0 \Rightarrow x^2(-36/6400)...
So \( x = 0 \) is the only solution — but this implies the circle is t...
At \( x = 0 \): \( y^2 = 64 \), so \( y = \pm8 \).
Check in ellipse: \( 0 + \frac{64}{64} = 1 \) — yes.
Now check if other intersections exist:
The circle has radius 8, ellipse semi-minor axis is 8 — so the circle...
But does it intersect in more points? No — since the circle lies entir...
Actually, the circle is inscribed: at \( x=0 \), both have \( y = \pm8...

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