Respuesta :

kelis123
Step  1  :Isolate a square root on the left hand side :

     Original equation 
     4 = √-6-2x+√31-3x

     Isolate
     -√-6-2x = -4+√31-3x

      Tidy up 
     √-6-2x = 4-√31-3x

Step  2  :Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√-6-2x)2 = (4-√31-3x)2

     After squaring 
     -6-2x = 31-3x+16-8√31-3x

Step  3  :Get remaining radical by itself :

     Current equation 
     -6-2x = 31-3x+16-8√31-3x

     Isolate radical on the left hand side
     8√31-3x = 6+2x+31-3x+16

      Tidy up 
     8√31-3x = 53-x

Step  4  :Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (8√31-3x)2 = (53-x)2

     After squaring 
     1984-192x = x2-106x+2809

Step  5  :Solve the quadratic equation :

     Rearranged equation
     x2  + 86x  + 825 = 0

     This equation has two rational roots:
       {x1, x2}={-11, -75}
 

Step  6  :Check that the first solution is correct :

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -11 for  x 
      √-6-2•(-11) = 4-√31-3•(-11)

      Simplify
      √16 = -4
      Solution does not check 
      4 ≠ -4 

Step  7  :Check that the second solution is correct :

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in  -75 for  x 
      √-6-2•(-75) = 4-√31-3•(-75)

      Simplify
      √144 = -12
      Solution does not check 
      12 ≠ -12 

Hopefully this helped You

Otras preguntas