Question

if x=2+√3 then x-1/x is equal to​

Answer 1

Answer:

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Step-by-step explanation:

\sf{GIVEN:-}GIVEN:−

x = 2 + √3

1/x = 1/(2 + √3) * (2 - √3)/(2 - √3)

1/x = (2 - √3)/(4 - 3)

[ (a - b)(a + b) = (a² - b²) ]

1/x = (2 - √3)

now,

x + 1/x = (2 + √3) + (2 - √3)

x + 1/x = 2 + 2 + √3 - √3

x + 1/x = 4

Answer 2

given

$x = 2 + \sqrt{3}$

we can Write

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} }$

rationalizing denominator we get

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

Now

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