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Re: If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ? [#permalink]

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19 Dec 2011, 01:14

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Instead of going the algebraic way , I think the quickest way is the method of substitution. Just replace x=2 in both the cases , and the answer comes as 9 is 20 secs.
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If x + 2/x = 3 what is the value of x^3 + 8/x^3 = ?

A) 1 B) 8 C) 9 D)16

Hi,

two other ways to do it..

1) Exploiting the choices.. whenever we have a^3+b^3, it is div by a+b.. and a^3-b^3 is div by a-b..

here \(x^3 + \frac{8}{x^3} = x^3 + (\frac{2}{x})^3\) should be div by\(x+\frac{2}{x}\), which is 3.. so \(x^3 + \frac{8}{x^3}\) should be multiple of 3.. so 9 should be the answer, as no other choice is miltiple of 3

2) formula \(a^3+b^3= (a+b)^3-3ab(a+b)\).. \(x^3 + \frac{8}{x^3} = x^3 + (\frac{2}{x})^3\)= \((x+\frac{2}{x})^3-3(x*\frac{2}{x}*( x+\frac{2}{x}))\).. =>\(3^3-3*2*3=27-18=9\) ans C
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Instead of going the algebraic way , I think the quickest way is the method of substitution. Just replace x=2 in both the cases , and the answer comes as 9 is 20 secs.

How did u come to a conclusion to substitute 2? why not other nos?

Hi ArunpriyanJ,

The post that you have quoted is from 2011 and I am sure the poster will not reply so let me pitch in The person might have started picking numbers randomly from 1 and luckily 2 is the number that fits here. This is just a brute force method and there is no set pattern here for number picking.