Solve the equation ##x^\frac{17}{6} + x^\frac{21}{25} =15##

AI Thread Summary
The discussion focuses on solving the equation x^(17/6) + x^(21/25) = 15, exploring various methods such as Newton's method, Brent's method, and Halley's method for their effectiveness. Participants note that Newton's method is efficient, while also questioning the reliability of Brent's and Halley's methods. Excel's goal seek feature is mentioned as a quick setup option, though it may complicate larger calculations. The conversation emphasizes the need for general methods to address equations with fractional exponents. Overall, the thread highlights the search for robust numerical solutions to complex equations.
chwala
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Homework Statement
Solve the equation ##x^\frac{17}{6} + x^\frac{21}{25} =15##

This is my original question (set by me).
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What about Brent's method and Halley's method? Are they reliable? I don't hear much about them.
 
Excel goal seek is quick to set up EDIT: but may be more difficult to incorporate into a bigger calc

$$\begin{array}{|c|c|c|c|}
\hline X&X**(17/6)&X**(21/25)&sum \\
\hline 2.463664029&12.86710567&2.132693501&14.99979917 \\
\hline
\end{array}$$
 

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