solving an equation with a radical

Question

solve the equation: the square root of x+2 - the square root of 2x+3 = -1

Answer 1

 

                  Hi Julia  lets give this a try.....

 

              square root (x+2) -   square root  (2x+3)   =  -1

 

Now square both sides to get rid of the square-root sign...we have....

 

         (X+2)  -   (2x+3)  =1                                                                    

 

             X +2   -    2x   +3    =1

         +2x -2       +2x   -2     =1

     ______________________

          3x                     +1   =1

                                 -1       -1               Subtrtact 1

_________________________

       3x =                                0

      ____                               ___

        3                                    3               Divide  by 3

 

             X=      0                                                                                                                           

 

                                 CHECK: Substitute 0  for X  we have...

 

      Square Root (0+2)  - square root (2 (0) +3)   = -1     (Square both sides)

 

   = (0+2)  -(2(0) +3   =  -1

 

          2        -3                   =  -1

 

              -1                 =  -1