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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: 54493
Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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28 Mar 2018, 11:00
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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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Re: If 5 - 6/x = x, then x has how many possible values?  [#permalink]

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31 Mar 2019, 00:24
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Re: If 5 - 6/x = x, then x has how many possible values?   [#permalink] 31 Mar 2019, 00:24

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