Question

if x=2-√3 find the value of (x+1/x)3​

Answer 1

Answer:

the correct answer is 8

Answer 2

Answer:

Hey mate!

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Given :

x = 2 - \sqrt{3}x=2−

3

To find :

(x - \frac{1}{x} ) {}^{3}(x−

x

1

)

3

Solution :

$$\begin{lgathered}x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{(2) {}^{2} - ( \sqrt{3} ) {}^{2} } \\ \\ \frac{1}{x} = \frac{2 + \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = 2 + \sqrt{3}\end{lgathered}$$

Now,

$$\begin{lgathered}x - \frac{1}{x} = 2 - \sqrt{3} - 2 - \sqrt{3} \\ \\ x - \frac{1}{x} = - 2\sqrt{3}\end{lgathered}$$

And,

$$\begin{lgathered}(x - \frac{1}{x} ) {}^{3} \\ \\ - (2 \sqrt{3} ) {}^{3} \\ \\ \therefore \boxed {\bold{- 24 \sqrt{3}}}\end{lgathered}$$