Question

m-1/m= 5 find m²+1/m² and m⁴+1/m⁴​

Answer 1

Step-by-step explanation:

$\sf m - \frac {1}{m} = 5 \\ \\ \sf squaring \:on\:both\:sides \\ \\ \sf { (m - \frac{1}{m})}^{2} = {5}^{2} \\ \\ \sf {m}^{2} - 2× m×\frac{1}{m} + \frac{1}{{m}^{2}} = 25 \\ \\ \sf {m}^{2} + \frac{1}{{m}^{2}} = 25 + 2 = 27 \\ \\ \sf Further \:squaring \:on\:both\:sides \\ \\ \sf { ( {m}^2 + \frac{1}{{m}^{2}} )}^{2} = {27}^{2} \\ \\ \sf {m}^{4} + 2 × {m}^{2} × \frac{1}{{m}^{2}} + \frac{1}{{m}^{2}} = 729 \\ \\ \sf {m}^{4} + 2 + \frac{1}{{m}^{4}} = 729 \\ \\ \sf {m}^{4} + \frac{1}{{m}^{4}} = 727$

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