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

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Joined: 14 Oct 2018
Posts: 18
Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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Updated on: 02 Jun 2019, 08:59
2
00:00

Difficulty:

65% (hard)

Question Stats:

56% (01:40) correct 44% (02:21) wrong based on 71 sessions

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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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02 Jun 2019, 05:49
1
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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02 Jun 2019, 08:45
1
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

Posted from my mobile device

$$(4x)^1/2 – (5)^1/2 = (3)^1/2$$

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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02 Jun 2019, 08:50
1
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

Posted from my mobile device

It's C. Bunuel kindly edit.
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Posts: 1829
Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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02 Jun 2019, 08:53
1
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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02 Jun 2019, 08:59
LeoN88 wrote:
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

Posted from my mobile device

It's C. Bunuel kindly edit.

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Edited the OA. Thank you.
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Posts: 199
Re: Solve for x: (4x)^(1/2) – 5^(1/2) = 3^(1/2)  [#permalink]

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