一、无理方程的增根出现的两种情况解无理方程时,一般采用方程两边分别同次乘方的方法,将其变形为有理方程,进而求出根来。方程两边同次乘方,实际上就是方程两边同乘以某个含有未知数的无理式(称之为有理化因式)。因此,有产生增根的可能。下面我们来讨论无理方程增根出现的两种情况。为确定起见,以仅含有二次根式的无理方程为例。自然,我们在实数范围内求解无理方程。一种情况是增根作为有理化因式等于零的根出现的。比如,无理方程 First, the two cases of increasing roots of irrational equations When solving irrational equations, generally use the method of two sides of the equation with the same power, transform it into a rational equation, and then find the root. The same side power of the equation is actually the same side of the equation multiplied by some irrational formula containing unknowns (call it a rationalized factor). Therefore, there is a possibility of rooting. Let’s discuss two cases of increasing roots of irrational equations. For the sake of certainty, consider an irrational equation that contains only quadric roots as an example. Naturally, we solve irrational equations in the real range. One situation is that rooting occurs as a root with a rationalized factor equal to zero. For example, irrational equations