Question

please anyone solve this question it's urgent​

Answer 1

Answer:

${m}^{2} + \frac{1}{ {m}^{2} } = 11$

Step-by-step explanation:

${m}^{2} - 3m - 1 = 0 \\ \\ discriminant = {b}^{2} - ac \\ \\ = {( - 3)}^{2} - 4(1)( - 1) \\ \\ = 9 + 4 = 13 \\ \\ m = \frac{ - ( - 3) + \sqrt{13} }{2} \: \: \: \: \: \: \: \: \: m = \frac{ - ( - 3) - \sqrt{13} }{2} \\ \\ m = \frac{ ( 3) + \sqrt{13} }{2} \: \: \: \: \: \: \: \: \: m = \frac{ ( 3) - \sqrt{13} }{2} \\ \\ take \: \: \: m = \frac{ ( 3) + \sqrt{13} }{2} \\ \\ \\ then \: \: \: \frac{1}{m} = \frac{2}{3 + \sqrt{13} } \\ \\ m = \frac{2( 3 - \sqrt{13} )}{3 + \sqrt{13} } \times \frac{1}{3 - \sqrt{13} } \\ \\ m = \frac{2(3 - \sqrt{13} )}{9 - 13} \\ \\ m = \frac{3 - \sqrt{13} }{ - 2} \\ \\ m = \frac{ \sqrt{13} - 3}{2} \\ \\ \\ therefore \: \: \: m + \frac{1}{m} = \frac{3 + \sqrt{13} + \sqrt{13} - 3 }{2} = \sqrt{13} \\ \\ \\ now \: \: \: \: {m}^{2} + \frac{1}{ {m}^{2} } = { (m + \frac{1}{m} )}^{2} - 2 = { \sqrt{13} }^{2} - 2 \\ \\ = 13 - 2 \\ \\ = 11 \\ \\ therefore \: \: \: {m}^{2} + \frac{1}{ {m}^{2} } = 11$