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# If x is a real number such that x-7√x+4=14, what is the value of x?

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Manager
Joined: 24 Feb 2020
Posts: 165
Location: Italy
WE: Analyst (Investment Banking)
If x is a real number such that x-7√x+4=14, what is the value of x?  [#permalink]

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17 Apr 2020, 11:05
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15% (low)

Question Stats:

84% (01:56) correct 16% (01:12) wrong based on 25 sessions

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If x is a real number such that $$x-7\sqrt{x+4}=14$$, what is the value of x?

(A) 77
(B) 80
(C) 83
(D) 86
(E) 89
DS Forum Moderator
Joined: 19 Oct 2018
Posts: 1998
Location: India
Re: If x is a real number such that x-7√x+4=14, what is the value of x?  [#permalink]

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17 Apr 2020, 11:28
x-14 = $$7\sqrt{x+4}$$

All the options are integer, then $$7\sqrt{x+4}$$ must be an integer.

Only 77+4 is a perfect square.

Ravixxx wrote:
If x is a real number such that $$x-7\sqrt{x+4}=14$$, what is the value of x?

(A) 77
(B) 80
(C) 83
(D) 86
(E) 89
Re: If x is a real number such that x-7√x+4=14, what is the value of x?   [#permalink] 17 Apr 2020, 11:28