if x – 1/x = 5 , find the values of x^2 + 1/x^2 and x ^4 +1 /x ^4 ​

Question

if x – 1/x = 5 , find the values of x^2 + 1/x^2 and x ^4 +1 /x ^4

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Evelyn 2 days 2021-10-12T06:46:43+00:00 2 Answers 0 views 0

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    0
    2021-10-12T06:48:06+00:00

    \Large\underline\mathbb\blue{ANSWER}

     \tt{{x -  \frac{1}{x} } } =5

    On squaring both sides,

    \tt{{({x -  \frac{1}{x} })^{2}  } } ={(5 ) }^{2}  \\  \\  \implies \tt{ {(x)}^{2} + 2( \cancel{x})( \frac{1}{ \cancel{x}}   ) -  { (\frac{1}{x} )}^{2} } \\  \\  \implies \tt{ {x}^{2}   -   \frac{1}{ {x}^{2}  } = 27 }

    \tt{{( {x}^{2}   -   \frac{1}{ {x}^{2}  }) }^{2}  ={( 27) }^{2}  } \\  \\   \implies \tt{  { {x}^{4}  -  \frac{1}{{x }^{4} }+ 2 = {(27)}^2 }} \\  \\  \implies \tt{ {x}^{4}   -  \frac{1}{{x }^{4}  } = 729 - 2} \\  \\  \implies \tt{  \boxed{ \tt{ \pink{{x}^{4}  -  { \frac{1}{{x }^{4} }} = 727}}}}

    hope it’s helpful

    0
    2021-10-12T06:48:11+00:00

    Answer:

    Now,

    For first answer Steps

    Squaring both sides will give

    (x-1/x) ²=(5)²

    x²+1/x²-2=25 Using (a-b) ²= a²-2ab+b²

    x²+1/x²=27

    Now for second answer

    Again squaring both sides give

    (x²+1/x²) ²= (27)²

    x⁴+1/x⁴+2=729

    x⁴+1/x⁴=727

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