Solve the equation. check your answer

Question

Solve the equation. check your answer

 

√¯¯x+4+3=√¯¯3x + 1

 

the solution is x = ?

Answer 1

√(X +4) + 3 = √(3X +1)

 

 

[√( X +4) + 3 ] ^2 = (√3X +1 )^2

 

  

    X+4 + 9 + 6 √( X +4) = 3X +1

 

    X + 13 + 6 √( X + 4) = 3X +1

 

         2X - 12 = 6 √(X +4 )

 

          X - 6 = 3 √( X +4)

 

          X^2 - 12X + 36 = 9 ( X +4)

 

           X^2 -21X =0

 

           X ( X -21 ) =0

 

          X = 0    X =21

 

         Test:

 

        √(21 +4) + 3    √(3 . 21 +1)

 

             (√25+ 3=8 ) =  (√64 =8)

    

           X =0

 

      √( 0 +4) +3     √3(0) +1

 

                5     ≠      1    / Not acceptable