Question

If x = 2- √3, then find the value of x^3-1/x^3 . 



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Answer 1

Answer:

$x^{3}-1/x^{3}=\sqrt[-30]{3}$

Step-by-step explanation:

Given:

$x=2-\sqrt{3}$

So,

By rationalizing the denominators, we get,

$⇒[1(2+\sqrt{3})]/[(2-\sqrt{3})(2+\sqrt{3})]$

$⇒[(2+\sqrt{3})]/[(2^{2})-(\sqrt{3})^{2}]$

$⇒[(2+\sqrt{3})]/[4-3]$

$⇒2+\sqrt{3}$

Now,

$x-1/x=2-\sqrt{3}-2-\sqrt{3}$

$⇒-2\sqrt{3}$

Let us cube on both sides, we get,

$(x-1/x)^{3}=(-2\sqrt{3})^{3}$

$x^{3}-1/x^{3}-3(x)(1/x)(x-1/x)=\sqrt[24]{3}$

$x^{3}-1/x^{3}-3(-2/\sqrt{3})=\sqrt[-24]{3}$

$x^{3}-1/x^{3}+\sqrt[6]{3}=\sqrt[-24]{3}$

$x^{3}-1/x^{3}=\sqrt[-24]{3}-\sqrt[6]{3}$

$⇒\sqrt[-30]{3}$

Hence,

$x^{3}-1/x^{3}=\sqrt[-30]{3}$

Hope it helps.

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Answer 2

Answer:

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