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# If 5 - 6/x = x, then x has how many possible values?

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Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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28 Mar 2018, 11:00
1
Siddhuftr wrote:
Bunuel wrote:
If 5 - 6/x = x, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

$$5 - \frac{6}{x} = x$$;

$$\frac{5x - 6}{x} = x$$;

$$5x -6 = x^2$$;

$$(x-3)(x-2)=0$$;

$$x=3$$ or $$x=2$$.

Well i wanted to reconfirm , we eliminated the possibility of x=0 , because equating x=0 in the equation doesn't solve it , Right ??

x is not 0 because after solving the question we got that x = 3 or x = 2 and did not get that x = 0, which naturally means that x = 0 does not satisfy the given equation.

x cannot be 0 because x is in the denominator of one term, 6/x, and we cannot divide by 0. If x were 6/x would not be defined.
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Posts: 65
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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12 May 2019, 00:13
If $$5 - \frac{6}{x} = x$$, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

Ok. simplifying the expression:
5x-6=x^2=0
=>x^2-3x-2x+6=0
=>(x-3)(x-2)=0

So, x=2

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Manager
Joined: 13 Nov 2018
Posts: 128
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GMAT 1: 700 Q51 V32
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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28 Jun 2019, 04:44
If $$5 - \frac{6}{x} = x$$, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

5-6/x=x

5x-6=x^2;
x^2-5x+6=0

x=3 or x=2

Total sol:2
OA: C
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Joined: 03 Jun 2019
Posts: 1850
Location: India
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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15 Sep 2019, 05:46
If $$5 - \frac{6}{x} = x$$, then x has how many possible values?

(A) None
(B) One
(C) Two
(D) A finite number greater than two
(E) An infinite number

x^2-5x+6=0
x=2 or 3

IMO C

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Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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16 Oct 2019, 00:07
If b^2 - 4ac> 0 , then 2 solutions
If b^2 - 4ac=0, then 1 solution
If b^2 -4ac < 0, then undefined

Hope it helps
Re: If 5 - 6/x = x, then x has how many possible values?   [#permalink] 16 Oct 2019, 00:07

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