Question

If a=2 - 3^1/2 then find (a - 1/a)^3​

Answer 1

Answer:

$\left(a-\frac{1}{a}\right)^{3}=-24\sqrt{3}$

Step-by-step explanation:

Given a = 2-√3 ---(1)

$\frac{1}{a}= \frac{1}{2-\sqrt{3}}\\=\frac{(2+\sqrt{3})}{(2-\sqrt{3})(2+\sqrt{3})}\\=\frac{(2+\sqrt{3})}{2^{2}-(\sqrt{3})^{2}}\\=\frac{(2+\sqrt{3})}{4-3}\\=\frac{(2+\sqrt{3})}{1}\\=2+\sqrt{3}$

$a-\frac{1}{a}\\=2-\sqrt{3}-(2+\sqrt{3})\\=2-\sqrt{3}-2-\sqrt{3}\\= -2\sqrt{3}$

$Now,\\\left(a-\frac{1}{a}\right)^{3}\\=(-2\sqrt{3})^{3}\\=-24\sqrt{3}$

Therefore,

$\left(a-\frac{1}{a}\right)^{3}=-24\sqrt{3}$

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