Question

If x=2-√3 then (x+1/x)^2 is​

Answer 1

If x=2-√3 then (x+1/x)^2 is 4

Step-by-step explanation:

$( x + \frac{1}{x} ) ^{2}$

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

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

$(2 - \sqrt{3} + \frac{2 + \sqrt{3} }{ {2}^{2} - ( \sqrt{3} )^{2} } )$

$(2 - \sqrt{3} + \frac{2 + \sqrt{3} }{ {4} - 3})$

(2-√3 + 2+√3)

4

Answer 2

Step-by-step explanation:

x=2-√3

x=2+

3

To find :

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

x

1

Solution :

\begin{gathered}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{gathered}

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{gathered}x + \frac{1}{x} \\ \\ = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ = 2 + 2 \\ \\ = 4\end{gathered}

x+

x

1

=2+

3

+2−

3

=2+2

=4