[SOLVED] Does not give all solutions

[Tim Wessman]

(07-12-2016 11:54 AM)CH3791 Wrote:  However, the HP Prime only gives 1.318. Why?

Specifically, when you put in the ".25" you are telling the CAS "I am doing this calculation in an approximate way using non-exact numbers". Thus when it starts solving things, it switches to a numerical method to isolate a result and you end up with one result within the range you gave. Numerical solution methods as a general rule work on the "try the calculation, check the result, scoot the input up/down a bit, check the result again" and so on until you converge to a numerical value that is close enough to a result.

Any numerical value containing a decimal is a "non-exact" number. Thus something like 4 / 5 is actually very different then 4. / 5 from the CAS point of view. One is the fraction of two exact integer values and represents the "concept" of 4/5. The other is an approximated value of four, divided by the perfect integer value of 5 and the result of that calculation is and approximate value of .8

To ensure the CAS won't approximate, keep decimal approximations out of your inputs. Either put in 1/4 (which is an exact mathematical representation of that number), or surround your fraction with exact(.25) which converts the decimal to a fraction beforehand.