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Mathematics Algebra Equation Solving Symbolic Computations

How to obtain such a result when solving the system of equations?

Bill Blair

Posted 4 days ago

Clear[f] f[x_] = 2 E^(2 x) - a (x - 1) Reduce[{f[x1] == 0, f[x2] == 0}, a, Reals] The desired final result is as shown below: a == (E^(2 x2) - E^(2 x1))/(x2 - x1)

POSTED BY: Bill Blair

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Gianluca Gorni

Gianluca Gorni, University of Udine

Posted 4 days ago

Your desired final result does not seem to follow from the premises: Clear[f, x, x1, x2, a]; f[x_] = 2 E^(2 x) - a (x - 1); twoConds = f[x1] == 0 && f[x2] == 0; thirdCond = a == (E^(2 x2) - E^(2 x1))/(x2 - x1); counterExample = {x1 -> 2, x2 -> 1 - 1/2 ProductLog[-(2/E^2)], a -> 2 E^4}; {twoConds, thirdCond} /. counterExample // Simplify

Your desired final result does not seem to follow from the premises:

Clear[f, x, x1, x2, a];
f[x_] = 2 E^(2 x) - a (x - 1);
twoConds = f[x1] == 0 && f[x2] == 0;
thirdCond = a == (E^(2 x2) - E^(2 x1))/(x2 - x1);
counterExample = {x1 -> 2, x2 -> 1 - 1/2 ProductLog[-(2/E^2)], 
   a -> 2 E^4};
{twoConds, thirdCond} /. counterExample // Simplify

POSTED BY: Gianluca Gorni