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How to solve the parameters

How to solve the parameters

Examples of the parameters - a special kind of mathematical problems requiring not quite the standard approach in the decision.



Since the parameters may be as equations and inequalities. In either case, we need to express X.

Simply examples of this type it is not made explicitly, and through this same parameter.
Parameter itself, more precisely, its value - anumber. Options usually denoted by the letter a. But the problem is that we do not know his unit, no sign. This gives rise to difficulties in dealing with inequalities or disclosure modules.


Nevertheless, it is possible (but careful pre-marking all possible limitations) to apply all the usual methods of working with equations and inequalities.
And, in principle, the expression itself through x and usually does not take much time and effort.
But the full answer writing - is much more laborious and time-consuming process.


The fact is that due to the ignorance of the value of the parameter, we are obliged to consider all possible cases and for all values ​​from minus to plus infinity.
Here it is very useful to a graphical method. Sometimes called "coloring". It lies in the fact that we axes x (a) (or (x) - a convenient) depict lines derived from transformation of our original example. And then we begin to work with these lines: as the value of a is not fixed, then we need a line containing in its equation parameter shift schedule, parallel tracking and calculating the points of intersection with other lines, as well as analyzing the areas of signs: they are suitable to us or no. Suitable for convenience and clarity, will shade.
Thus, we go through the entire axis from minus to plus infinity, checking the answer for all a.


the answer is written similar to the answer for himselfmethod of intervals with a caveat: we are not just specify a set of solutions for x, and write, and what set of values ​​corresponding to a set of values ​​of x.

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