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Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)

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Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post Updated on: 02 Jun 2019, 08:59
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A
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C
D
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Question Stats:

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Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)

A) (2+√15)/2
B) (2+√15)
C) (4+√15)/2
D) (4+√15)
E) None of the above

Originally posted by Rajat1998 on 02 Jun 2019, 05:21.
Last edited by Bunuel on 02 Jun 2019, 08:59, edited 1 time in total.
Edited the OA.
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 02 Jun 2019, 05:49
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IMO C ,


take √5 to right side and square both side
u get option C


Could you explain why the OA is A .


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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 02 Jun 2019, 08:45
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Rajat1998 wrote:
Solve for x:\((4x)^1/2 – (5)^1/2 = (3)^1/2\)

A) (2+√15)/2
B) (2+√15)
C) (4+√15)/2
D) (4+√15)
E) None of the above

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\((4x)^1/2 – (5)^1/2 = (3)^1/2\)

Or, \((4x)^1/2 = (3)^1/2 + (5)^1/2\)

Or, \(4x = 3 + 5 + 2*√15\) {Squaring both sides}

Or, \(4x = 8 + 2*√15\)

Or, \(x = \frac{8 + 2*√15}{4}\)

Or,\(x = 2 + \frac{√15}{2}\)


Now, Check option (C) \(\frac{(4+√15)}{2}\) = \(2 + \frac{√15}{2}\)

Hope this helps...
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 02 Jun 2019, 08:50
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Rajat1998 wrote:
Solve for x: (4x)^1/2 – (5)^1/2 = (3)^1/2

A) (2+√15)/2
B) (2+√15)
C) (4+√15)/2
D) (4+√15)
E) None of the above

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It's C. Bunuel kindly edit.
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 02 Jun 2019, 08:53
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Yes, the answer should be C here:

√(4x) = √3 + √5
4x = (√3 + √5)^2
4x = 3 + 5 + 2√15
4x = 8 + 2√15
2x = 4 + √15
x = (4 + √15)/2
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 02 Jun 2019, 08:59
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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New post 14 Jun 2019, 07:08
(4x)^1/2 = 3^1/2 + 5^1/2

4x = 8 + 15^1/2

x= (2 + 15^1/2)/2
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Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)   [#permalink] 14 Jun 2019, 07:08
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