Question

x=2+ root 3 find
(x+1/x)2

Answer 1

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

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