Question

x+1/x = 2+√3,Find the value of
x^2 +1/x ^2

Answer 1

Answer:

$x + \frac{1}{x} = 2 + \sqrt{3} \\ \\ \sf squaring \: both \: sides - \\ \\ (x + \frac{1}{x} )^{2} = (2 + \sqrt{3} ) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 2 {}^{2} + \sqrt{3} {}^{2} + 2 \times 2 \times \sqrt{3} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 4 + 3 + 4 \sqrt{3} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 7 + 4 \sqrt{3} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 7 + 4 \sqrt{3} - 2 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 5 + 4 \sqrt{3}$

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