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    Perturbation Theory

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

    © BrainMass Inc. brainmass.com March 4, 2021, 5:44 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/perturbation-theory-equation-8410

    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. The real root of the equations are analyzed.

    $2.19

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