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If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =

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If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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New post Updated on: 01 May 2020, 10:18
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A
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C
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Question Stats:

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If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} =\frac{ w}{z}\), then\( w = \)

A. \(z + 1 \)

B. \(z^2 + 1\)

C. \(-z^2 + 1\)

D. \(-z^2 + z + 1\)

E. \(-2z^2 + 1\)

PS14031.02

Originally posted by gmatt1476 on 20 Apr 2020, 10:21.
Last edited by carcass on 01 May 2020, 10:18, edited 1 time in total.
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Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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New post 20 Apr 2020, 10:28
1
gmatt1476 wrote:
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = w/z\), then w =

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02



\(z + \frac{1 - 2z^2}{z} = w/z\)

=> \(z(z + \frac{1 - 2z^2}{z}) = w\)

=> \(w = z^2 + (1 - 2z^2)\)

=> \(w = 1 - z^2\)

Answer C
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Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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New post 28 Apr 2020, 07:38
Top Contributor
gmatt1476 wrote:
If z ≠ 0 and \(z + \frac{1 - 2z^2}{z} = \frac{w}{z}\), then \(w =\)

A. z + 1
B. z^2 + 1
C. -z^2 + 1
D. -z^2 + z + 1
E. -2z^2 + 1

PS14031.02


Given: \(z + \frac{1 - 2z^2}{z} = \frac{w}{z}\)

Eliminate the fractions, multiply both sides of the equation by \(z\) to get: \(z^2 + (1 - 2z^2) = w\)

Simplify to get: \(1 - z^2 = w\)

Rewrite as: \(-z^2 + 1= w\)

Answer: C

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If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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New post 29 May 2020, 09:46
Assume any value of z
Let z=1
=> w = 0
Now check where w= 0 for z=1 in the option
(a) w=2
(b) w=2
(C) w= 0.
(D) w=1
(e) w= -1

Therefore, (c) is the correct option.

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Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =  [#permalink]

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New post 30 May 2020, 05:12

(z^2 + 1-2z^2)/z = w/z

z^2 + 1 -2z^2 = w

1 - z^2 = w

Option C


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Re: If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =   [#permalink] 30 May 2020, 05:12

If z ≠ 0 and z + (1 - 2z^2)/z = w/z, then w =

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