Which value(s) of $x$ satisfies the equation above?

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Fri Dec 10, 2021 4:31 am

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$2x-2=\sqrt{3x^2+13}$

Which value(s) of $x$ satisfies the equation above?

I. $-1$
II. $4$
III. $9$

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

Answer: B

Source: Magoosh

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Source: Beat The GMAT — Problem Solving | Fri Dec 10, 2021 4:31 am

regor60: Master | Next Rank: 500 Posts; Posts: 416; Joined: Thu Oct 15, 2009 11:52 am; Thanked: 27 times

Re: Which value(s) of $x$ satisfies the equation above?

by regor60 » Fri Dec 10, 2021 5:06 am

Since I appears in all the answer choices but B, potentially eliminating this would immediately identify the answer:
Plugging in -1 into the right side:

(3*(-1^2)+13)^(1/2) = (3+13)^(1/2)=
16^(1/2) = 4

Does this result equal the left side?

2*-1 -2 = -4 > NO

AnswerB

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