+0  
 
+1
282
8
avatar+606 

Hi guys,

 

just a question please. This sum:

 

\(x^{2 \over3}-20=44\)

\(x^{2 \over3}=64\)

\(x^{({1 \over3})^2}=64\)

Let K = \(x^{1 \over3}\)

So \(K^2=8^2\)

Therefore K = 8

 

Sub back:

\(x^{1 \over3}=8\)

\(x^{1 \over3}=2^3\)

\(x=2^{3*3} \)

\(x=512\)

 

Tis is my reasoning. I am led to believe this is wrong and HAS to be done this way:

 

\(K^2-64=0\)

\((K-8)(k+8)=0\)

\(K=8\) or \(K=-8\)

\((x^{1 \over3})^3=8^3\)     or      \((x^{1 \over3})^3=-8^3\)

x=512                          x= -512

 

Why must it be done this way?..why two answers?

 Apr 5, 2019
 #1
avatar+24454 
0

x^(2/3) = 64     take sqrt of both sides

 

x^1/3 = + - 8     Cube both sides

x = 512   or -512  

 Apr 5, 2019
 #2
avatar+109723 
+3

The only thing I can see wrong with your logic is that you that if

x^2 =64

x can be poitive or negative 8

 

other than that, your way is fine.  :)

 

 

\(x^{2 \over3}-20=44\\ \left( x^{\frac{1}{3}}\right)^{2}=64\\ x^{\frac{1}{3}}=\pm8\\ x=8^3 \qquad or \qquad x=(-8)^3\\ x=512 \qquad or \qquad x=-512\\ \)

.
 Apr 5, 2019
 #3
avatar+111392 
+1

x^(2/3) - 20 = 44

 

x^(2/3) = 64

 

(x^2)^(1/3) = 64    cube both sides

 

x^2  = 64^3

 

x^2 = 262144    take both roots

 

x =  ±  √262144

 

x = ± 512

 

cool cool cool

 Apr 5, 2019
 #5
avatar+1015 
-3

Yeah All the top people who answer questions the most are answering Awsome.... smiley

Nickolas  Apr 5, 2019
 #4
avatar
+1

x^(2/3) ⇒ (-512)^(2/3) = 64 (-1)^(2/3) ≈ -32. + 55.4256 i    ?????

 Apr 5, 2019
 #6
avatar+109723 
+3

x^(2/3) ⇒ (-512)^(2/3) = 64 (-1)^(2/3) ≈ -32. + 55.4256 i    ?????

 

that is not correct

 

x^(2/3)

when x=-512

⇒ (-512)^(2/3)

= (64) *(-1)^(2/3)   true

 

       (-1)^(2/3) = [(-1)^2]^(1/3) = [1]^(1/3) = 1

       or

      (-1)^(2/3) = [   (-1)^(1/3)   ]^(2) = [-1]^(2) = 1

      either way

 

= (64) *(-1)^(2/3) 

=  +64

 

 

I am glas you showed us your confusion.  People do not learn if they do not ask questions  :)

Melody  Apr 5, 2019
 #7
avatar+606 
+3

yep yep....I have it...a square root ALWAYS has a positive and negative answer...my my...how could I forget that????.....Thank you to all who replied..I do appreciate..

juriemagic  Apr 5, 2019
 #8
avatar+109723 
+2

We know you appreciate us Juriemagic that is why we are always quick to answer your questions.

(At least we try to be and I think we usually are)

 

I always appreciate your good manners too  laugh

Melody  Apr 5, 2019

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