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# Find all its solutions. (|2*Z|)!–|Z|=Z

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SVP
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Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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19 Jun 2003, 00:10
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Find all its solutions. (|2*Z|)!–|Z|=Z
SVP
Joined: 03 Feb 2003
Posts: 1604
Followers: 9

Kudos [?]: 268 [0], given: 0

Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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19 Jun 2003, 22:41
now it is correct.
it is imperative that you sovle the question, not simply guess it.

Manager
Joined: 24 Jun 2003
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Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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26 Jun 2003, 06:45
The LHS equation always gives positive values. Therefore, solution cannot lie in Z<0

Now for Z>=0, the equation can be rewritten as

(2Z)!-Z=Z

which gives (2Z-1)!=1 which is only possible for
(2Z-1) = 0 or 1. This leads to values of Z as 1 or 1/2
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Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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24 Oct 2014, 12:39
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Manager
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Re: Find all its solutions. (|2*Z|)!–|Z|=Z [#permalink]

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25 Oct 2014, 00:03
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(|2*Z|)!–|Z|=Z

since |2z|!>|z|, LHS has to be >0, therefore RHS(Z)>0
|2z|!-|z|=z
|2z|!=z+|z|
|2z|!=2z
2z*(2z-1)=2z
since z>0, cancel 2z from both sides
2z-1=1
2z=2
z=1
Re: Find all its solutions. (|2*Z|)!–|Z|=Z   [#permalink] 25 Oct 2014, 00:03
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