# IndicesWatch

#1
Just wondering if anyone can tell me the answers to this and how to get to them, me and a mate have been trying this for a while and got nowhere

x^2/3 - x^1/3 - 2 =0

0
12 years ago
#2
Let

Then you've a quadratic in y, solve that then work out x from that.
0
12 years ago
#3
I think I'm right in saying

x^(2/3) - x^(1/3) -2 = 0

x^(1/3) = cubic root of x

Let cubic root of x = ax

2ax - ax - 2 = 0
ax - 2 = 0

Therefore the cubic root of x = 2

Cube both sides

x = 2^3
x = 8
0
12 years ago
#4
(Original post by vector771)
Let cubic root of x = ax
Why?
(Original post by vector771)
2ax - ax - 2 = 0
That's not what you get, you should get .

My method gives the quadratic so

So x = -1 or 2. Your method gets one of the right answers by doing two incorrect things.
0
12 years ago
#5
(Original post by vector771)
I think I'm right in saying

x^(2/3) - x^(1/3) -2 = 0

x^(1/3) = cubic root of x

Let cubic root of x = ax

2ax - ax - 2 = 0
ax - 2 = 0

Therefore the cubic root of x = 2

Cube both sides

x = 2^3
x = 8
I think you've made a mistake. I get
not
Factorising this gives

Edit: beaten to it.
0
12 years ago
#6
[QUOTE=AlphaNumeric]Why?
QUOTE]
I think he is just doing a similar thing to what you did AlphaNumeric, but using different notation (ax instead of y)

mebbe.!
0
12 years ago
#7
Okay, that explains the crap notation he uses (use a different symbol, not something involving x!) but not the doubling instead of squaring.
0
12 years ago
#8
I dont think thats the end of it
So youve got y = 2 or -1
but y = cubed root of x
so x = 8 or -1
0
12 years ago
#9
Okay, that explains the crap notation he uses (use a different symbol, not something involving x!)
I agree that the notation isn't very user friendly, but it is no worse than several other notation styles I can think of (such as the f(x) notation). I'd definitely stick to using a different letter though if I was trying to work it out from scratch.
0
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