MHB Can a Non-Integer Exponent be Used to Solve a Polynomial Equation?

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The discussion centers on solving the polynomial equation B.x^b - x - A = 0, where A, B, and b are constants. It is noted that if b is an integer not exceeding 4, algebraic solutions exist; otherwise, numerical methods are required. Since b is confirmed to be a non-integer, the consensus is that the equation will need to be solved numerically. Participants emphasize the limitations of algebraic solutions for non-integer exponents. Numerical methods are deemed the necessary approach for this type of polynomial equation.
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Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks
 
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NY99 said:
Not sure if this is the right place but could somebody help me solve the following equation
B.x^b - x - A =0 wher A, B and b are constants.
Thanks

Welcome on MHB NY99!...

... if b is integer not exceeding 4, then it exist a procedure for algebraic solutions ... otherwise generally the solutions have to be found numerically ... the same is if b is not an integer...

Kind regards

$\chi$ $\sigma$
 
Thanks for that. Unfortunately b is not an integer so I guess It will have to be numerically solved.
 
Thread 'How to define a vector field?'

Thread 'How to define a vector field?'

Hello! In one book I saw that function ##V## of 3 variables ##V_x, V_y, V_z## (vector field in 3D) can be decomposed in a Taylor series without higher-order terms (partial derivative of second power and higher) at point ##(0,0,0)## such way: I think so: higher-order terms can be neglected because partial derivative of second power and higher are equal to 0. Is this true? And how to define vector field correctly for this case? (In the book I found nothing and my attempt was wrong...
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