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anybody has a quick approach to this one for the value of N: [#permalink ]
22 Apr 2007, 10:33
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anybody has a quick approach to this one for the value of N:
|NтАУ|N+1||=|NтАУ2|

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o If n+1 >= 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N - N -1| = |N-2|
<=> 1 = |N-2|
<=> N=3 or N = 1
o If n+1 =< 0, then
|NтАУ|N+1||=|NтАУ2|
<=> |N + N+1| = |N-2|
<=> |2*N+1| = |N-2|
<=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0
<=> N = -3
Thus, N = -3 or N=1 or N=3

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techjanson wrote:

Fig wrote:

o If n+1 >= 0, then |NтАУ|N+1||=|NтАУ2| <=> |N - N -1| = |N-2| <=> 1 = |N-2| <=> N=3 or N = 1 o If n+1 =< 0, then |NтАУ|N+1||=|NтАУ2| <=> |N + N+1| = |N-2| <=> |2*N+1| = |N-2| <=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0 <=> N = -3 Thus, N = -3 or N=1 or N=3

Excellent explanation. Thanks!

Thanks to u

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Fig wrote:

o If n+1 >= 0, then |NтАУ|N+1||=|NтАУ2| <=> |N - N -1| = |N-2| <=> 1 = |N-2| <=> N=3 or N = 1 o If n+1 =< 0, then |NтАУ|N+1 ||=|NтАУ2| <=> |N + N+1 | = |N-2| <=> |2*N+1| = |N-2| <=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0 <=> N = -3 Thus, N = -3 or N=1 or N=3

Can you please explain the step in red color?

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fresinha12 wrote:

FIG: you are the abs, mod King

Thanks

... I just hope it helps to clarify it

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goalsnr wrote:

Fig wrote:

o If n+1 >= 0, then |NтАУ|N+1||=|NтАУ2| <=> |N - N -1| = |N-2| <=> 1 = |N-2| <=> N=3 or N = 1 o If n+1 =< 0, then |NтАУ|N+1 ||=|NтАУ2| <=> |N + N+1 | = |N-2| <=> |2*N+1| = |N-2| <=> -(2*N+1) = -(N-2) as 2*N+1 < 0 and N-2 < 0 <=> N = -3 Thus, N = -3 or N=1 or N=3

Can you please explain the step in red color?

Ok

In the second case, we have n+1 =< 0. Thus, we have |n+1| = -(n+1) : an absolute must always be positive or equal to 0.

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Himalayan wrote:

anybody has a quick approach to this one for the value of N: |NтАУ|N+1||=|NтАУ2|

what does NтАУ and NтАУ2 mean here?

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same question as above

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Is there a quant guru that could explain this question in more depth?

I don't understand the transition ...

"If n+1 >= 0, then

|NтАУ|N+1||=|NтАУ2|

<=> |N - N -1| = |N-2|"

Why?

Thanks in advance,

a

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Himalayan wrote:

anybody has a quick approach to this one for the value of N: |NтАУ|N+1||=|NтАУ2|

I guess the symbol (-ve sign) has been changed into something else. The question should be as under:

Quote:

What is the value of N: |N - |N+1||=|N - 2|

Work out from the inside modulus

The possibilities for : (1) If (N+1) >= 0 (2) If (N+1) <= 0

(1) If (N+1) >= 0

|N - N -1| = |N - 2|

|-1| = |N - 2|

1 = |N - 2|

N = 1 or 3

(2) If (N+1) <= 0

|N+N+1| = |N - 2|

|2N+1| = |N - 2|

(i) 2N +1 = N - 2

2N - N = - 3

N = -3

(ii) 2N +1 = N - 2

2N +1 = - N + 2

2N + N = 1

N = 1/3

(ii) - 2N -1 = - N + 2

-N = 3

N = -3

N = -3, 1/3, 1, & 3.

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