Share
Explore BrainMass

Perturbation Theory

Find the real root of the equation x^5 + ex - 1= 0 approximately to O(^2) using perturbation theory.

Solution Preview

Solution. We assume that the root x is of the following form
x=a+e*b
So, x^5=(a+e*b)^5=a^5+5*e*a^4*b+10*e^2*a^3*b^2+10*e^3*a^2*b^3+
5*e^4*a*b^4+b^5
So, the equation x^5+ex-1=0 is becoming
...

Solution Summary

Real roots are found using perturbation theory.

$2.19