Search 72,284 tutors FIND TUTORS
Search for tutors
Ask a question
0 0

(x-1)^2 = (x-2)^2

Tutors, please sign in to answer this question.

3 Answers

There are two possibilities:
x-1=x-2
x-1=2-x
 
First equation does not have any solutions. Second one gives x=3/2.
 
Or you can expand both sides.
x2-2x+1=x2-4x+4
From this you will get, by moving numbers to the right, and x-containing terms to the left:
x2-2x-x2+4x=4-1
2x=3
x=3/2

Comments

You're welcome any time!

Comment

( x-1) ^2 = ( x-2) ^2
 
 Take the square root of both sides:       If you expand both sides:
 
   X - 1 = + ( X-2) , no answer               X^2 -2X + 1 = X^2 -4x +4
 
    X -1 = - ( x-2)                                  -2x + 4X  = 4 - 1
 
      x -1 = -x +2                                    2X = 3
 
     2X = 3                                              X = 3/2
 
    X = 3/2 
Nisya:
 
The first thing I would do is "unravel" the factored expressions on each side of the equation, by multiplying out each side, as follows:
 
(x-1)2=(x-2)2
x2-2x+1=x2-4x+4
 
Next (by subtracting) I would bring all the terms with x to the left side and all non-x terms to the right side as follows:
 
x2-x2  -2x+4x  =  4-1
   0     +   2x     =    3
               2x     =    3
 
Finally solve for x, by dividing both sides by 2 to get:
 
x=3/2
 
You can check you work, by plugging 3/2 in for the value of x in the original expression:
 
(x-1)2=(x-2)2
(3/2-1)2=(3/2-2)2
(3/2-2/2)2=(3/2-4/2)2
(1/2)2=(-1/2)2
1/4=1/4 (check!)
 
Goo Luck!
 
George