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Home » Take natural log: −0.5t < ln(1/99) = −ln(99) ≈ −4.595 - 500apps

Take natural log: −0.5t < ln(1/99) = −ln(99) ≈ −4.595 - 500apps

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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u^4 + 3 = (u^2 - 2u + 2)Q(u) + au + b
To find \( a \) and \( b \), perform polynomial division or use substi...
Letâs use the roots of \( u^2 - 2u + 2 = 0 \). The discriminant is \...
u = rac{2 \pm \sqrt{-4}}{2} = rac{2 \pm 2i}{2} = 1 \pm i
Let \( lpha = 1 + i \), \( eta = 1 - i \). Then at \( u = lpha \):
lpha^4 + 3 = alpha + b
First compute \( lpha^2 \):
lpha = 1 + i \Rightarrow lpha^2 = (1+i)^2 = 1 + 2i + i^2 = 1 + 2i -...
lpha^4 = (lpha^2)^2 = (2i)^2 = 4i^2 = -4
lpha^4 + 3 = -4 + 3 = -1 = a(1+i) + b = a + ai + b

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