Anonymous

x = 2 or x = -1 OR implies that at least one answer is correct. It doesn't mean that both are correct. That is why you have to verify your answers. x =2 2 = 2 --> ok x^2 =4 4 = 4 --> ok x = 2 -1 = 2 --> no x^2 = 2 1 = 2 --> no erroneous result

Anonymous

x = 2 x + 2 = 4 --- eq (1) x^2 = 4 --- eq (2) eq (1) = eq (2) x + 2 = x^2 x^2 - x - 2 = 0 (x - 2) (x + 1) = 0 x = 2 or x = -1 sub x = -1 into eq(1), (-1) + 2 = 4 1 = 4 --> No False sub x = -1 into eq(2) (-1)^2 = 4 1 = 4 --> No False

Anonymous

x = -1 is an extraneous solution, so x = 2.

Anonymous

Both equations 1 and 2 come from the original step. Therefore, if you change the value of the original x (which is what you do when you use x = -1), then it changes BOTH equations 1 and 2. With x = -1, you get x + 2 = 1 x^2 = 1 Therefore, the bad step is the combination of substituting only in equation 1 without applying the same substitution to equation 2 (they are both from the same initial condition).

Anonymous

x = 2 or x = -1 obviously you take x = 2, your original equation says x = 2. -1 ≠ 2