Question

if x = 2 + root 3, find the value of x square + 1 by x square

Answer 1

x = 2+ √3 

x² = (2 + √3)² 

x² = 4 + 3 + 2(2√3)

x² = 7 + 4√3 

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1/x = 1/(2 + √3)



      By Rationalization,

1/x = (2 - √3)/[2² - (√3)²]

1/x =(2 - √3)/(4 -3)

1/x = (2 - √3 )/1

1/x = 2 - √3 

1/x² = (2 - √3)²

1/x² = 4 + 3 - 2(2√3)

1/x² = 7 - 4√3


                      Then,

x²  + 1/x²

⇒ 7 + 4√3 + 7 - 4√3

⇒ 7 + 7

⇒ 14 



i hope this will help you



(-:

Answer 2

Solution:-

given by:-

$x = 2 + \sqrt{3} \\ {x}^{2} + \frac{1}{ {x}^{2} } \\ {(2 + \sqrt{3}) }^{2} + \frac{1}{ {(2 + \sqrt{3} )}^{2} } \\ \frac{(2 + 3 + 4 \sqrt{3} )(2 + 3 + 4 \sqrt{3}) + 1 }{(2 + \sqrt{3}) } \\ \frac{4 + 6 + 8 \sqrt{3 } + 6 + 12 \sqrt{3} + 8 \sqrt{3} + 12 \sqrt{3} + 48 + 1}{(2 + \sqrt{3}) } \\ \frac{65 + 40 \sqrt{3} }{(2 + \sqrt{3} )} \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \frac{130 + 80 \sqrt{3} - 65 \sqrt{3} - 120 }{4 - 3} \\ \frac{10 + 15 \sqrt{3} }{1} \\ (10 + 15 \sqrt{3} )ans$