In solving certain of equations, one may obtain besides the proper () roots (http://planetmath.org/Equation) also some strange roots which do not satisfy the original equation. Such a thing can happen especially when one has in some stage squared both sides of the treated equation; in this situation one must check all “roots” by substituting them to the original equation.
Substituting these values of into the left side of the original equation yields
Thus, only is valid, is a strange root. (How is related to the solved equation, is explained by that it may be written , from which one would obtain via the quadratic formula that , i.e. or . The latter corresponds the value , but it were relevant to the original equation only if we would allow negative values for square roots of positive numbers; the practice excludes them.)
The general explanation of strange roots when squaring an equation is, that the two equations
are not equivalent (http://planetmath.org/Equivalent3) (but the equations and would be such ones).
|Date of creation||2013-03-22 17:55:53|
|Last modified on||2013-03-22 17:55:53|
|Last modified by||pahio (2872)|