AngouriMath
SolveByRationalisingASumOfRoots(AngouriMath.Entity,AngouriMath.Entity.Variable,System.Boolean)
Method (no overloads)
Summary
A denominator factor that is a sum or difference of two square roots of
polynomials, multiplied above and below by its conjugate:
(1 + x)/(sqrt(x^2 + 2x + 4) - sqrt(x^2 + x + 1)) is
(1 + x)(sqrt(x^2 + 2x + 4) + sqrt(x^2 + x + 1))/(x + 3) , the product of the
pair being the difference of the radicands -- and each of the two terms is then a
root of a quadratic beside a rational function, Euler's. Timofeev's.
polynomials, multiplied above and below by its conjugate:
pair being the difference of the radicands -- and each of the two terms is then a
root of a quadratic beside a rational function, Euler's. Timofeev's.
Remarks
Two roots only: a polynomial beside one root, x + sqrt(x^2 + 1) , is Euler's
substitution itself, and answered more shortly as that. The conjugate is nonzero
wherever the factor is, and(a - b)(a + b) = a^2 - b^2 holds for the
principal roots as for any values, so nothing is assumed about signs. Once: the
respelling has no such factor left.
https://github.com/asc-community/AngouriMath/issues/718
substitution itself, and answered more shortly as that. The conjugate is nonzero
wherever the factor is, and
principal roots as for any values, so nothing is assumed about signs. Once: the
respelling has no such factor left.
https://github.com/asc-community/AngouriMath/issues/718
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