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# If x > 0, what is the value of x ?

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Joined: 01 Sep 2010
Posts: 3453

Kudos [?]: 9766 [0], given: 1238

If x > 0, what is the value of x ? [#permalink]

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26 Jul 2017, 08:05
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69% (00:46) correct 31% (00:50) wrong based on 198 sessions

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If x > 0, what is the value of x ?

(1) $$x^3 – x = 0$$

(2) $$\sqrt[3]{x} - x = 0$$
[Reveal] Spoiler: OA

_________________

Kudos [?]: 9766 [0], given: 1238

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139468 [0], given: 12790

Re: If x > 0, what is the value of x ? [#permalink]

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26 Jul 2017, 08:19
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If x > 0, what is the value of x ?

(1) $$x^3 – x = 0$$. Since x is not 0, we can safely reduce by x:

$$x^2 - 1 = 0$$

$$x^2 = 1$$

$$x = 1$$ or $$x = -1$$ (discard since $$x > 0$$).

So, $$x = 1$$ only. Sufficient.

(2) $$\sqrt[3]{x} - x = 0$$

$$\sqrt[3]{x} =x$$

$$x = x^3$$

$$x^3 – x = 0$$.

The same as in (1). Sufficient.

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Kudos [?]: 139468 [0], given: 12790

Intern
Joined: 10 Sep 2014
Posts: 19

Kudos [?]: [0], given: 294

Re: If x > 0, what is the value of x ? [#permalink]

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07 Dec 2017, 10:03
Dear Bunuel can you please clarify "^3√x=x, then x=x^3" how the interchange occurred? and I had x=1 in the statement 1 which made that sufficient, but what value do Statement 2 has to make it sufficient? Not getting this part in statement 2 "x^3–x=0. The same as in (1). Sufficient".

Kudos [?]: [0], given: 294

Math Expert
Joined: 02 Sep 2009
Posts: 43322

Kudos [?]: 139468 [1], given: 12790

Re: If x > 0, what is the value of x ? [#permalink]

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07 Dec 2017, 10:19
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Expert's post
Dear Bunuel can you please clarify "^3√x=x, then x=x^3" how the interchange occurred? and I had x=1 in the statement 1 which made that sufficient, but what value do Statement 2 has to make it sufficient? Not getting this part in statement 2 "x^3–x=0. The same as in (1). Sufficient".

(2) $$\sqrt[3]{x} - x = 0$$

$$\sqrt[3]{x} =x$$

Take to the third power: $$x = x^3$$

$$x^3 – x = 0$$. Since x is not 0, we can safely reduce by x:

$$x^2 - 1 = 0$$

$$x^2 = 1$$

$$x = 1$$ or $$x = -1$$ (discard since $$x > 0$$).

So, $$x = 1$$ only. Sufficient.
_________________

Kudos [?]: 139468 [1], given: 12790

Re: If x > 0, what is the value of x ?   [#permalink] 07 Dec 2017, 10:19
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