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Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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27 Apr 2017, 23:41

F(x + 1/x) = (x + 1/x)^2 - 2 So, the function can easily be reduced to F(y) = y^2 - 2 where y = x + 1/x Therefore, F(4) + F(5) = (4^2-2) + (5^2-2) = 14 + 23 = 37 Pick D

Re: IF F(x + 1/x) = x^2 + 1/x^2....what is the value of [#permalink]

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21 May 2017, 02:07

keats wrote:

F(x + 1/x) = (x + 1/x)^2 - 2 So, the function can easily be reduced to F(y) = y^2 - 2 where y = x + 1/x Therefore, F(4) + F(5) = (4^2-2) + (5^2-2) = 14 + 23 = 37 Pick D

Can someone please provide a better explanation? Thanks in advance!

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If we square \(x + \frac{1}{x}\) we will get \(x^2 + \frac{1}{x^2} + 2\). So we can write \(F(x + \frac{1}{x})\) = \((x +\frac{1}{x})^2\) - 2 = \(x^2 + \frac{1}{x^2}\) ---> F(4) = (4)^2 - 2 = 14 and F(5) = (5)^2 - 2 = 23 Adding, 37.
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