Question

if x = 2-√3, find the value of x-1\x​

Answer 1

Answer:

Answer:

4

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

44

Step-by-step explanation:

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