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Home » The least common multiple of the cycle lengths is \(\boxed24\).**Question: - Veritas Home Health

The least common multiple of the cycle lengths is \(\boxed24\).**Question: - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 \[ x^2 - 4x + 3 = 0 \]

📌 \[ (x - 1)(x - 3) = 0 \]

📌 Solutions: \( x = 1 \) or \( x = 3 \).

📌 A ladder 13 meters long leans against a wall, reaching a height of 12 meters. How far is the base from the wall?

📌 Using Pythagoras:

📌 \[ x^2 + 12^2 = 13^2 \]

📌 \[ x^2 + 144 = 169 \]

📌 \[ x^2 = 25 \]

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Now try \( u = eta = 1 - i \):
eta^2 = (1 - i)^2 = 1 - 2i + i^2 = 1 - 2i - 1 = -2i
eta^4 = (-2i)^2 = 4i^2 = -4
eta^4 + 3 = -1 = a(1 - i) + b = a - ai + b
Imaginary part: \( -a = 0 \Rightarrow a = 0 \), then \( b = -1 \)
So both give \( a = 0 \), \( b = -1 \)
Conclusion: the remainder is constant \( -1 \)
Alternatively, polynomial division confirms:
Divide \( u^4 + 0u^3 + 0u^2 + 0u + 3 \) by \( u^2 - 2u + 2 \)
First: \( u^4 \div u^2 = u^2 \), multiply: \( u^2(u^2 - 2u + 2) = u^4...

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