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

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

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26 Jul 2017, 09:05
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If x > 0, what is the value of x ?

(1) $$x^3 – x = 0$$

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

(DS17543)

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

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26 Jul 2017, 09:19
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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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Re: If x > 0, what is the value of x ?  [#permalink]

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07 Dec 2017, 11:19
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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.
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Re: If x > 0, what is the value of x ?  [#permalink]

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07 Dec 2017, 11:03
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".
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Re: If x > 0, what is the value of x ?  [#permalink]

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25 Oct 2018, 14:07
carcass wrote:
If x > 0, what is the value of x ?

(1) $$x^3 – x = 0$$

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

(DS17543)

This is basically Tautology in which the statements are repeated and yield the same answer.

$$x^3 - x = 0$$

$$x ( x^2 - 1) = 0$$

$$x ( x - 1) (x + 1) = 0$$

x > 0 so it can be -1 or 0 x = 1

For statement 2)

We square both sides we get $$x^3 - x = 0$$

Then the same goes on.

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

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30 Nov 2019, 07:18
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Re: If x > 0, what is the value of x ?   [#permalink] 30 Nov 2019, 07:18
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