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

Question

Solve for x.  I know you have to extract the roots, but I'm not sure about the +/-

Answer 1

( 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 

Answer 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

Answer 3

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