In details

Irrational equations


Consider the following equations:

Note that they all have variable or unknown in the root. These equations are irrational. That is:

Irrational equation is any equation that has variable in the radicating.

Resolution of an irrational equation

The resolution of an irrational equation must be done by trying to transform it initially into a rational equation, obtained by raising both members of the equation to a convenient power.

Then we solve the found rational equation and finally check whether or not the roots of the rational equation obtained can be accepted as roots of the given irrational equation (check equality).

This check is necessary, because as we raise the two members of an equation to a power, they can appear in the equation obtained. strange roots to the given equation. Note some examples of solving irrational equations in the set of reals.


  • Solution:

    Thus, V = {58}.

  • Solution:

    Thus, V = {-3}; note that 2 is a root foreign to this irrational equation.

  • Solution:

    Thus, V = {7}; note that 2 is a root foreign to this irrational equation.

  • Solution:

    Thus, V = {9}; note that It is a strange root to this irrational equation.
Next: Systems of Equations of the 2nd Degree