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# If x+(1/x)=4, what is the value of x^2+(1/x^2)?

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If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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12 Oct 2018, 07:38
00:00

Difficulty:

15% (low)

Question Stats:

86% (00:31) correct 14% (01:00) wrong based on 29 sessions

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[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})$$?

$$A. 4$$
$$B. 10$$
$$C. 12$$
$$D. 14$$
$$E. 16$$

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If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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12 Oct 2018, 07:52
$$(a+b)^2$$ = $$a^2$$ + $$b^2$$ +2ab.

Here a = x and b = $$\frac{1}{x}$$.

Substituting this, we get.

$$(x+\frac{1}{x})^2$$ = $$x^2$$ + $$\frac{1}{x}^2$$ +2x$$\frac{1}{x}$$.

16-2 = $$x^2$$ + $$\frac{1}{x}^2$$

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If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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12 Oct 2018, 11:43
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})$$?

$$A. 4$$
$$B. 10$$
$$C. 12$$
$$D. 14$$
$$E. 16$$

FOCUS:

$$? = {x^2} + {1 \over {{x^2}}}$$

DATA:

$$x + {1 \over x} = 4\,\,\,\,\left( * \right)$$

FOCUS-DATA CONNECTION:

$$?\,\, = \,\,{x^2} + \underline 2 + {1 \over {{x^2}}} - \underline 2 \,\, = \,\,{\left( {x + {1 \over x}} \right)^2} - 2\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{4^2} - 2 = 14$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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12 Oct 2018, 23:23
fskilnik wrote:
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})$$?

$$A. 4$$
$$B. 10$$
$$C. 12$$
$$D. 14$$
$$E. 16$$

FOCUS:

$$? = {x^2} + {1 \over {{x^2}}}$$

DATA:

$$x + {1 \over x} = 4\,\,\,\,\left( * \right)$$

[color=#0000ff]FOCUS-DATA CONNECTION:

$$?\,\, = \,\,{x^2} + \underline 2 + {1 \over {{x^2}}} - \underline 2 \,\, = \,\,{\left( {x + {1 \over x}} \right)^2} - 2\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{4^2} - 2 = 14$$
[/color]

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

How did you get -2 there?

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 52902
Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)?  [#permalink]

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13 Oct 2018, 01:12
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If $$x+(\frac{1}{x})=4$$, what is the value of $$x^2+(\frac{1}{x^2})$$?

$$A. 4$$
$$B. 10$$
$$C. 12$$
$$D. 14$$
$$E. 16$$

Discussed here: https://gmatclub.com/forum/if-x-1-x-4-x ... fl=similar
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Re: If x+(1/x)=4, what is the value of x^2+(1/x^2)?   [#permalink] 13 Oct 2018, 01:12
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