Question

x=(2+√3),find the value of x²+1/x²

Answer 1

Heya !!

Here's your answer..
_______________________________

x = 2 +√3

$\frac{1}{x} = \frac{1}{2 + \sqrt{3} } \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{4 - 3} \\ \\ \frac{1}{x} = \frac{2 - \sqrt{3} }{1} \\ \\ x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} \\ \\ x + \frac{1}{x} = 4 \\ \\ take \: \: square \: \: both \: \: side \: \: \\ \\ {(x + \frac{1}{x}) }^{2} = {(4)}^{2} \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14$

______________________________

Hope it helps..
thanks :)

Answer 2

X²+1/x² = (2+√3)²+1/(2+√3)² = (4+3+4√3)+1/(4+3+4√3) = (7+4√3)+1/(7+4√3) = (7+4√3)²+1/(7+4√3) = (49+48+56√3+1)/(7+4√3) = [(98+56√3)/(7+4√3)]×[(7-4√3)/(7-4√3)] = [(98+56√3)(7-4√3)]/7²-(4√3)² = (686+392√3-392√3-672)/(49-48) = 14/1 = 14
Hope it helps to you.