Tip 26. Begin with a symbol but finish by a number  Fig. 26. Begin with a symbol but finish by a number

In tip 24 we try to solve the system of algebraic equations using diagram method – we have defined the domain of existence of real roots of the system, we have found the values of the unknowns for first approximation for search of the solution using numerical method that will be done in tip 44. But it is possible and necessary to try to put in a «symbol» in the line «graph – number». The main point of the tip is the following. It is worth to apply tools of symbolic mathematics of Mathcad for solution a problem before using numerical method. Analytic solution of our system of two nonlinear algebraic equations (see tip 24) with the help of Mathcad-operators solve and float is showed in the fig. 26. (Here we use not one operator solve but the couple solve – float as since one operator solve often gives either very bulky answer or nothing). All 24 roots are found but for of them (1, 6, 19 and 22) are real ones. They are reflected on the graph in tip 24.

Only five signs in fixed point part (see the key float, 5) are outputted in the answer in the fig. 26. By default (without the key float) 20 signs are outputted but their maximum quantity is 250. (The command of the same name from the menu Symbolic (the command Solve on Variable) can give up to 4 000 signs in fixed point part. However the command works only with the equations but not with the systems of equations.)

The roots can be outputted in the form of decimal fraction with floating point (0.043778) but not in the «scientific» form (4.3778×10-2), if we enclose the expression in the fig. 26 by cursor and press the key «=». After this it is possible to format corresponding way already «numerical» answer (see also tip 3).

 The operator solve gives the answer in the form of matrix, which has the same quantity of columns as the system has the unknowns but the quantity of lines equals the quantity of roots. The function Find is able to give an answer in more difficult form – in the form of embedded array (see tip 77).