Problem

$\begin{array}{c}\sqrt{ } t^{3}+1 \\ =\left(\frac{y^{4}+1}{y^{2}+1}\right)^{5}\end{array}$

Answer

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Answer

Solve for t in terms of y: \(t = \boxed{(-1 + \frac{(y^4 + 1)^{10}}{(y^2 + 1)^{10}})^{\frac{1}{3}}}\)

Steps

Step 1 :Simplify the equation: \(\sqrt{t^3 + 1} = \left(\frac{y^4 + 1}{y^2 + 1}\right)^5\)

Step 2 :Solve for t in terms of y: \(t = \boxed{(-1 + \frac{(y^4 + 1)^{10}}{(y^2 + 1)^{10}})^{\frac{1}{3}}}\)

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