+0

# Why

+1
282
8

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
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
+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
+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   Apr 5, 2019
#5
-3

Yeah All the top people who answer questions the most are answering Awsome.... Nickolas  Apr 5, 2019
#4
+1

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

Apr 5, 2019
#6
+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) = ^(1/3) = 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
+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
+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 Melody  Apr 5, 2019