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If sq rt (3-2x) = sq rt (2x) + 1.....

This topic has 1 expert reply and 2 member replies
chendawg Master | Next Rank: 500 Posts
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If sq rt (3-2x) = sq rt (2x) + 1.....

Post Sun Mar 06, 2011 1:57 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If sq rt (3-2x) = sq rt (2x) + 1, then 4x^2=

    A. 1
    B. 4
    C. 2 - 2x
    D. 4x - 2
    E. 6x - 1

    Source: OG 12

    OA after some discussion.

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    Post Sun Mar 06, 2011 3:30 pm
    chendawg wrote:
    If sq rt (3-2x) = sq rt (2x) + 1, then 4x^2=

    A. 1
    B. 4
    C. 2 - 2x
    D. 4x - 2
    E. 6x - 1

    Source: OG 12

    OA after some discussion.
    Since none of the answer choices contains a √, we need to perform algebra that will clear all the √ symbols:

    √(3-2x) = √2x + 1

    [√(3-2x)]² = (√2x + 1)²

    3 - 2x = (√2x + 1)(√2x + 1)

    3 - 2x = 2x + √2x + √2x + 1

    2 - 2x = 2x + 2√2x

    1 - x = x + √2x

    1 - 2x = √2x

    (1 - 2x)² = (√2x)²

    (1 - 2x)(1 - 2x) = 2x

    1 - 2x - 2x + 4x² = 2x

    4x² = 6x - 1.

    The correct answer is E.

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    anshumishra Legendary Member
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    Post Sun Mar 06, 2011 3:40 pm
    chendawg wrote:
    If sq rt (3-2x) = sq rt (2x) + 1, then 4x^2=

    A. 1
    B. 4
    C. 2 - 2x
    D. 4x - 2
    E. 6x - 1

    Source: OG 12

    OA after some discussion.
    √(3-2x) - √2x = 1; square both sides
    => 3-2x + 2x - 2√(3-2x)(2x) = 1
    => 2√(3-2x)(2x) = 2
    => √(3-2x)(2x) = 1; square both sides
    => (3-2x)*2x = 1
    => 6x - 4x^2 = 1
    => 4x^2 = 6x - 1, E

    _________________
    Thanks
    Anshu

    (Every mistake is a lesson learned )

    chendawg Master | Next Rank: 500 Posts
    Joined
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    Posted:
    163 messages
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    4 members
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    7/8
    Target GMAT Score:
    760
    GMAT Score:
    660
    Post Wed Mar 09, 2011 8:33 am
    OA is indeed E.

    I'm not sure if I would be able to figure out to do another square under test conditions, is there a clue for future problems?

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