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Home » \( 15^4 = (-2)^4 = 16 - Blask

\( 15^4 = (-2)^4 = 16 - Blask

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Question: A renewable energy system’s efficiency is modeled by the equation $ \frac{a + 2b}{a - 2b} + \frac{a - 2b}{a + 2b} = 2 $. Find $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $.

📌 Solution: Let $ x = \frac{a + 2b}{a - 2b} $. Then the equation becomes:

📌 x + \frac{1}{x} = 2

📌 Multiplying both sides by $ x $:

📌 x^2 + 1 = 2x \Rightarrow x^2 - 2x + 1 = 0 \Rightarrow (x - 1)^2 = 0 \Rightarrow x = 1

📌 So $ \frac{a + 2b}{a - 2b} = 1 \Rightarrow a + 2b = a - 2b \Rightarrow 4b = 0 \Rightarrow b = 0 $

📌 Now compute $ \frac{a^2 + 4b^2}{a^2 - 4b^2} $. Since $ b = 0 $, this becomes:

📌 \frac{a^2}{a^2} = \boxed{1}

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\[ T^{\mu
u} = egin{pmatrix} \sigma & 0 & 0 & 0 \ 0 & 0 & 0 & 0 \ 0 & 0 & 0 & 0...
The trace of the tensor is:
\[ T^{\mu}_{\mu} = T^{0}_{0} + T^{1}_{1} + T^{2}_{2} + T^{3}_{3} = \si...
Under a Lorentz boost along the x-axis with velocity \(v\), the metric...
u} = ext{diag}(1, -1, -1, -1) \), and the transformation matrix \(\La...
\[ \Lambda = egin{pmatrix} \gamma & -\gamma v & 0 & 0 \ -\gamma v & \...
where \(\gamma = rac{1}{\sqrt{1-v^2}}\).
The transformed tensor is \( T'^{\mu
u} = \Lambda^\mu_{lpha} \Lambda^

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