Question

If x =7+4 root 3 then find the value of rootx+1/rootx

Answer 1

$\huge\mathfrak{Answer}$

$x = 7 + 4 \sqrt{3} \\ \frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \\ \frac{1}{x} = \frac{1}{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } \\ \: \: \: \: \: \: = \frac{7 - 4 \sqrt{3} }{ ({7})^{2} - ( {4 \sqrt{3}} ) ^{2} } \\ \: \: \: \: = \frac{7 - 4 \sqrt{3} }{49 - 48} \\ \: \: \: \: \: = 7 - 4 \sqrt{3} \\ x + \frac{1}{x} = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \\ x + \frac{1}{x} = 14$