Question

23 Rd one please fast

Answer 1

${m}^{2} - 4m + 1 = 0 \\ using \: std \: formula \\ m = 2 + \sqrt{3} \: \: or \: \: 2 - \sqrt{3}$
$taking \: \: m = 2 + \sqrt{3} \\ \frac{1}{m} = \frac{2 - \sqrt{3} }{(2 + \sqrt{3} )(2 - \sqrt{3}) } = 2 - \sqrt{3} \\ m + \frac{1}{m} = 4$
${m}^{3} + \frac{1}{ {m}^{3} } = {(m + \frac{1}{m} )}^{3} - 3(m + \frac{1}{m} ) \\ {4}^{3} - 3 \times 4 = 52$