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# If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2?

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Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? [#permalink]
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I would go for E.
Please show a quick way.

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Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? [#permalink]
It is pretty straight forward if dealt this way -

(r+1/r)^3 = r^3 +(1/r)^3 + 3(r*(1/r))(r+(1/r))
(r+1/r)^3 = r^3 +(1/r)^3 + 3(r+(1/r))

We know that r+(1/r) = (5)^1/2

So r^3 +(1/r)^3 = 2*(5^(1/2))
Square the ans = 20
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Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? [#permalink]
GMATGuruNY
(r + 1/r)² = 5
r + 1/r = √5

Hi GMATGuruNY

should not the highlighted part above be |r + 1/r| = √5

Why did you avoid modulus sign?
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Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? [#permalink]
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Mo2men
GMATGuruNY
(r + 1/r)² = 5
r + 1/r = √5

Hi GMATGuruNY

should not the highlighted part above be |r + 1/r| = √5

Why did you avoid modulus sign?

Since $$r + \frac{1}{r} = √5$$ yields one of the answer choices, there is no need to consider $$r + \frac{1}{r} = -√5$$.
Re: If (r+1/r)^2 = 5, what is the value of (r^3+1/r^3)^2? [#permalink]
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