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

[chwala]

Homework Statement

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

This is my original question (set by me).

Relevant Equations

Numerical methods

Would we also use Newton's method, or are there more powerful methods? Are there general methods for solving equations with fractional exponents?

The solution to this problem is;

https://www.wolframalpha.com/input?i=solve+x^(17/6)+++x^(21/25)+=+15

 

[fresh_42]

Newton-Raphson is already quite fast:
https://math.stackexchange.com/ques...y-of-newton-raphson-method-to-find-square-roo

 

[chwala]

What about Brent's method and Halley's method? Are they reliable? I don't hear much about them.

 

[gmax137]

Excel goal seek is quick to set up EDIT: but may be more difficult to incorporate into a bigger calc

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