σt^2=1/p(σp^2+1/s(σs^2+1/a(σa^2)))

Solve for σp

asked by guest
on Sep 20, 2024 at 3:26 am



You asked:

Given \(σ \cdot {t}^{2} = \frac{1}{p \cdot \left(σ \cdot {p}^{2} + \frac{1}{s \cdot \left(σ \cdot {s}^{2} + \frac{1}{a \cdot σ \cdot {a}^{2}}\right)}\right)}\) evaluate the expression \(σ p\).

MathBot Answer:

\(p σ \in \left\{- \frac{a^{3} σ}{2 p s \left(a^{3} s^{2} σ^{2} + 1\right)} - \frac{\sqrt{4 a^{6} s^{6} σ^{4} p + a^{6} t^{2} σ^{2} + 8 a^{3} s^{4} σ^{2} p + 4 s^{2} p}}{2 p s t \left(a^{3} s^{2} σ^{2} + 1\right)}, - \frac{a^{3} σ}{2 p s \left(a^{3} s^{2} σ^{2} + 1\right)} + \frac{\sqrt{4 a^{6} s^{6} σ^{4} p + a^{6} t^{2} σ^{2} + 8 a^{3} s^{4} σ^{2} p + 4 s^{2} p}}{2 p s t \left(a^{3} s^{2} σ^{2} + 1\right)}\right\}\)

$$\begin{aligned}t^{2} σ &= \frac{1}{p \left(p^{2} σ + \frac{1}{s \left(s^{2} σ + \frac{1}{a^{3} σ}\right)}\right)}\\p σ \left(p^{2} σ + \frac{1}{s \left(s^{2} σ + \frac{1}{a^{3} σ}\right)}\right) &= \frac{1}{t^{2}}\\p σ&=- \frac{a^{3} σ}{2 p s \left(a^{3} s^{2} σ^{2} + 1\right)} - \frac{\sqrt{4 a^{6} s^{6} σ^{4} p + a^{6} t^{2} σ^{2} + 8 a^{3} s^{4} σ^{2} p + 4 s^{2} p}}{2 p s t \left(a^{3} s^{2} σ^{2} + 1\right)}\end{aligned}$$

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