Question

If x= 2 − √3, then find the value of
$(x - \frac{1}{x}){2}$

​

Answer 1

Answer:

4

Step-by-step explanation:

Given :

x = 2 + \sqrt{3}x=2+

3

To find :

x + \frac{1}{x}x+

x

1

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}

x=2+

3

x

1

=

2+

3

1

×

2−

3

2−

3

x

1

=

(2)

2

−(

3

)

2

2−

3

x

1

=

4−3

2−

3

x

1

=2−

3

Now,

\begin{lgathered}x + \frac{1}{x} \\ \\ \implies 2 + \cancel{\sqrt{3}} + 2 - \cancel{ \sqrt{3}} \\ \\ \implies 2 + 2 \\ \\ \implies 4\end{lgathered}

x+

x

1

⟹2+

3

+2−

3

⟹2+2

⟹4