Question

If x=2+√3, the value of x+1/x is​

Answer 1

Answer:

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

3

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

x

1

Solution:

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

x

1

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

3

To find 1x\frac{1}{x}

x

1

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

3

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

x

1

=

(2)

2

−(

3

)

2

2−

3

1x=2−34−3\frac{1}{x}= \frac{2 -\sqrt{3}}{4 - 3}

x

1

=

4−3

2−

3

1x=2−3\frac{1}{x}= 2- \sqrt{ 3}

x

1

=2−

3

Substitute the values

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

x

1

2+3+2−32+\sqrt{3}+2- \sqrt{ 3}2+

3

+2−

3

444

Hence the value of x+1xx+\frac{1}{x}x+

x

1

is 4