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# if x<0, what is the value of ^1/4+(-x*|x|)^1/2 i guess

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VP
Joined: 25 Nov 2004
Posts: 1483
if x<0, what is the value of ^1/4+(-x*|x|)^1/2 i guess [#permalink]

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18 Jul 2006, 14:40
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if x<0, what is the value of [(x-3)^4]^1/4+(-x*|x|)^1/2

i guess it was discussed earlier. no OA.
Director
Joined: 06 May 2006
Posts: 791

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18 Jul 2006, 15:12

Using the newly learnt lesson that the root of any positive integer is its absolute value (which is positive).

Going by this logic, [(x-3)^4]^1/4 evaluates to (-x+3); and sqrt(-x|x|) evalutates to -x.

So we get (-x + 3) - x = 3 - 2x
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Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes

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18 Jul 2006, 17:33

Using the newly learnt lesson that the root of any positive integer is its absolute value (which is positive).

Going by this logic, [(x-3)^4]^1/4 evaluates to (-x+3); and sqrt(-x|x|) evalutates to -x.

So we get (-x + 3) - x = 3 - 2x

We can plug in any integer to check the ans.

if X = -1
[(-1-3)^4]^1/4+(1*|-1|)^1/2 = 5

3-2x = 3+2 = 5

So, we know 3-2x is correct!
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Intern
Joined: 20 Jun 2005
Posts: 27
Location: Santa Clara

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18 Jul 2006, 18:34
[(x-3)^4]^1/4 how does it evaluate to -x+3??

I thought 4 and 1/4 cancelled themselves.
Senior Manager
Joined: 22 May 2006
Posts: 368
Location: Rancho Palos Verdes
Re: How does it work? [#permalink]

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18 Jul 2006, 18:37
rajiv_av wrote:
[(x-3)^4]^1/4 how does it evaluate to -x+3??

I thought 4 and 1/4 cancelled themselves.

but we are given that x<0..

if you cancelled 4 and 1/4, you get |x-3| not x-3..

So x-3<0... |x-3| = -x+3
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GMAT Club Legend
Joined: 07 Jul 2004
Posts: 5043
Location: Singapore

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18 Jul 2006, 19:10
[(x-3)^4]^1/4+(-x*|x|)^1/2

-x+3 + (-x*|x|)^1/2

-x+3 + (x^2)^1/2

-x+3-x
-2x+3

We have to invert the signs because x is negative...
18 Jul 2006, 19:10
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