(2x+12)^2/3-3=13

Question

solve and check for extraneous solutions

 

Answer 1

A. (((2x+12)^2)/3)-3=13
((2x+12)^2)/3=16
(2x+12)^2=16*3
|2x+12|=4*sqrt(3)
2x+12=±4*sqrt(3)
x+6=±2*sqrt(3)
x=-6±2*sqrt(3)

B. ((2x+12)^(2/3))-3=13
((2x+12)^2)^(1/3))=16
(2x+12)^2=16^3
|2x+12|=16^(3/2)=64
2x+12=±64
x+6=±32
x=-6±32=-38 or 24

C. (2x+12)^((2/3)-3)=13
(2x+12)^(-7/3)=13
Raise both sides to -3/7 power:
(2x+12)=13^(-3/7)
2x=13^(-3/7)-12
x=(13^(-3/7))/2-6
x≈ -5.83344191822469

Answer 2

 [( 2X + 12) ^2] / 3  - 3 = 13

 

   ( 2X +12) ^2 = 48

 

    ( 2X +1 2 ) ^2 - 48 =0

 

   ( 2X +12 + 4 √3 ) ( 2X +12 - 4 √3 ) =0

 

    X = -12 -4√3      X = -12+4√3

                2                     2

 

    X = - 6 ± 2 √3

Answer 3

(2x + 12)^(2/3) - 3 = 13    [add 3]

(2x + 12)^(2/3) = 16    [exponentiate by 3/2]

2x + 12 = 16^(3/2)    [simplify]

2x + 12 = 64    [subtract 12]

2x = 52    [divide by 2]

x = 26

 

http://www.wolframalpha.com/input/?i=solve+%282x+%2B+12%29^%282%2F3%29+-+3+%3D+13

 

Now check to make sure the answer is not extraneous.
(2(26) + 12)^(2/3) - 3 = 13

(52 + 12)^(2/3) - 3 = 13

64^(2/3) - 3 = 13

16 - 3 = 13

13 = 13