Question

m+1/m=5 find [m²+1/m²]and [m⁴+1/m⁴]

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Answer 1

Answer:

${m}^{2} + \frac{1}{ {m}^{2} } = 23 \\ {m}^{4} + \frac{1}{ {m}^{4} } = 527$

Step-by-step explanation:

$m + \frac{1}{m} = 5 \\ squaring \: on \: both \: the \: sides \\ {(m + \frac{1}{m}) }^{2} = {(5)}^{2} \\ {(m)}^{2} + { (\frac{1}{m} )}^{2} + 2(m)( \frac{1}{m} ) = 25 \\ {m}^{2} + \frac{1}{ {m}^{2} } + 2 = 25 \\ {m}^{2} + \frac{1}{ {m}^{2} } = 25 - 2 \\ {m}^{2} + \frac{1}{ {m}^{2} } = 23 \\ squaring \: on \: both \: the \: sides \\ {( {m}^{2} + \frac{1}{ {m}^{2} }) }^{2} = {(23)}^{2} \\ { ({m}^{2} )}^{2} + {( \frac{1}{ {m}^{2} } )}^{2} + 2( {m}^{2} )( \frac{1}{ {m}^{2} } ) = 529 \\ {m}^{4} + \frac{1}{ {m}^{4} } + 2 = 529 \\ {m}^{4} + \frac{1}{ {m}^{4} } = 529 - 2 \\ {m}^{4} + \frac{1}{ {m}^{4} } = 527$