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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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New post 12 Oct 2018, 07:38
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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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New post 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 = \(x^2\) + \(\frac{1}{x}^2\)

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

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New post 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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New post 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
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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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New post 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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