Question

if x =2+√3 find the value of x-1/x .​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

SOLUTION

GIVEN

$\displaystyle \sf{x = 2 + \sqrt{3} }$

TO DETERMINE

$\displaystyle \sf{x - \frac{1}{x} }$

EVALUATION

Here it is given that

$\displaystyle \sf{x = 2 + \sqrt{3} }$

Now

$\displaystyle \sf{ \frac{1}{x} }$

$\displaystyle \sf{ = \frac{1}{2 + \sqrt{3} } }$

$\displaystyle \sf{ = \frac{2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3} )} }$

$\displaystyle \sf{ = \frac{2 - \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } }$

$\displaystyle \sf{ = \frac{2 - \sqrt{3} }{ 4 - 3 } }$

$\displaystyle \sf{ = \frac{2 - \sqrt{3} }{ 1} }$

$\displaystyle \sf{ = 2 - \sqrt{3} }$

Now we have

$\displaystyle \sf{x - \frac{1}{x} }$

$\displaystyle \sf{ = (2 + \sqrt{3}) - (2 - \sqrt{3}) }$

$\displaystyle \sf{ = 2 + \sqrt{3} - 2 + \sqrt{3} }$

$\displaystyle \sf{ = 2 \sqrt{3} }$

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