Question

if x = 1/2+√3 then x -1/x is equal to:​

Answer 1

Answer:

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Answer 2

Solution:

$\longrightarrow\sf{x = \dfrac{1}{2 + \sqrt{3}}}$

Now, we are going to use the method of rationalization. In this method, we will remove the radical sign present in √3.

$\longrightarrow\sf{x = \dfrac{1(2 -\sqrt{3})}{(2 + \sqrt{3})(2 - \sqrt{3})}}$

On the denominator side, algebraic identity is used. We know that:

$\implies\bf{(a + b)(a - b) = a^2 - b^2}$

By applying, we get:

$\longrightarrow\sf{x = \dfrac{2 -\sqrt{3}}{(2^2 - \sqrt{3}^2)}}$

$\longrightarrow\sf{x = \dfrac{2 -\sqrt{3}}{(4 - 3)}}$

$\longrightarrow\sf{x = \dfrac{2 -\sqrt{3}}{1}}$

$\longrightarrow\sf{x = 2 - \sqrt{3}}$

We know that,

$\longrightarrow\sf{x = \dfrac{1}{2 + \sqrt{3}}}$

Therefore,

$\longrightarrow\sf{\dfrac{1}{x} = 2+ \sqrt{3}}$

According to the question,

$\longrightarrow\sf{x - \dfrac{1}{x} = (2- \sqrt{3}) - (2 + \sqrt{3})}$

$\longrightarrow\sf{x - \dfrac{1}{x} = 2- \sqrt{3} -2 - \sqrt{3}}$

$\longrightarrow\sf{x - \dfrac{1}{x} = -2 \sqrt{3}}$

Hence, this is our final answer. The method of rationalization has made our simplifications easier than normal calculations by taking LCM.