Question

If x=2+√3, find (x+1/x)3​

Answer 1

Step-by-step explanation:

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

3

To Find : find the value of x+\frac{1}{x}x+

x

1

Solution:

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

x

1

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

3

To find \frac{1}{x}

x

1

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

3

\frac{1}{x} =\frac{1}{2 +\sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3}}

x

1

=

2+

3

1

×

2−

3

2−

3

\frac{1}{x} =\frac{2 -\sqrt{3} }{(2) {}^{2} - ( \sqrt{3}) {}^{2} }

x

1

=

(2)

2

−(

3

)

2

2−

3

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

x

1

=

4−3

2−

3

\frac{1}{x}= 2- \sqrt{ 3}

x

1

=2−

3

Substitute the values

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

x

1

2+\sqrt{3}+2- \sqrt{ 3}2+√3 + 2 - √3 4 Hence the value of ×+1-× is 4.