Why 1 is an extraneous solution? I can verify it by squaring √1=-1 and obtain 1=1 . Why it is wrong?
The reason 1 is not a solution is that √(5x-4)=x-2 is not true when x is replaced by 1: √(5*1-4)=1, while 1-2 = -1.After solving you get: (x-8)(x-1)=0. Why 1 is an extraneous solution? I can verify it by squaring √1=-1 and obtain 1=1 . Why it is wrong?
Thank you dr. Peterson and lookagain for your answers. So basically if there aren't hidden terms i can't square equations because that could lead to extraneous values. Is it an algebra rule? or common sense?No, you cannot square both sides after that. You
are evaluating each side separately in the check to see if they are equal. \(\displaystyle \ \sqrt{1} = 1. \ \ \) That ends
the simplifying on the left-hand side. Now you
have (are looking at) 1 = -1, which is false. So,
you must discard x = 1 as a solution.