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Home » Le rayon \( r \) du cercle inscrit est donnÃ© par : - Londonproperty

Le rayon \( r \) du cercle inscrit est donnÃ© par : - Londonproperty

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Letâs now expand and factor directly:

📌 x^4 + 8x^2 + 16 - 16y^4 + 64 = x^4 + 8x^2 + 80 - 16y^4

📌 Now factor $ x^4 + 8x^2 + 80 $:

📌 Try factoring as $ (x^2 + a)^2 + b $, or test rational root theorem. Letâs try factoring by grouping:

📌 x^4 + 8x^2 + 80 = x^2(x^2 + 8) + 80

📌 Not helpful. Try factoring as a quadratic in $ x^2 $:

📌 Let $ u = x^2 $, then:

📌 u^2 + 8u + 80 = (u + 4)^2 + 64

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We need to place 4 H’s into these 4 gaps, with **at most one H per gap...
There is only **one** way to choose positions: H in each gap → so the...
H P H P H P H → i.e., H P H P H P H
But wait — this places H in all 4 gaps, but total positions:
Each gap holding one H gives:
positions: H (1), P (2), H (3), P (4), H (5), P (6), H (7) → exactly 7...
So the structure is uniquely determined: H in positions 1,3,5,7 and P...
No other configuration allows 4 non-adjacent H’s in 7 positions.
Thus, only **one** such sequence satisfies the condition.
But wait — is that correct? Let's verify:

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× 18 = 153.86 × 10 = 1,538.6, 153.86 × 8 = 1,231.08 → total 2,769.68 →...
× 10 = 1,538.6 — no: 153.86 × 18
150×18=2,700, 3.86×18=69.48 → total 2,769.48 → ÷10 = 276.948
Same.
So 276.948 → rounds to 277.
But in the context of research, maybe keep as 276.95? But format expec...
Given prior examples are integers, and this is estimation, we’ll use:
But to be precise, and since clean answer, perhaps the problem expects...
Alternatively, use π=22/7 ≈ 3.143 → 3.14 is given, so follow.
Final decision: compute and round to nearest integer.

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