If x = 7 + 4√3, find the value of x^4 + (1/x^4).

Question

If x = 7 + 4√3, find the value of x^4 + (1/x^4).

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Aaliyah 2 weeks 2021-09-07T12:56:27+00:00 2 Answers 0 views 0

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    0
    2021-09-07T12:57:44+00:00

    Answer:

    x=7+4√3

    1/x=1/7+4√3

    =1/7+4√3×7-4√3/7-4√3

    =7-4√3/1

    =7-4√3

    x^4+1/x^4

    =(7+4√3)^4+(7-4√3)^4

    =((7+4√3)^2)^2 +((7-4√3)^2)^2

    =(97+56√3)^2+ (97-56√3)^2

    =2((97)^2+(56√3)^2)

    =2(9409+9408)

    =37,634

    x^4+1/x^4 =37,634

    hope this helps you mark me as brainliest pls

    0
    2021-09-07T12:57:52+00:00

    Answer:Hey mate !


    _______________________



    Given :



    x = 7 + 4√3



    To find :



    √x + 1 / √x



    Solution :



    x = 7 + 4√3



    ⇒ x = 4 + 3 + 4√3



    ⇒ x = 2² + √3² + 2 × 2 × √3



    ⇒ x = ( 2 + √3)²



    ⇒ √x = 2 + √3



    Now,



    1 / √x = 1 / 2 + √3 × 2 – √3 / 2 – √3



    ⇒ 1 / √x = 2 – √3 / 2² – √3²



    ⇒ 1 / √x = 2 – √3 / 4 – 3



    ⇒ 1 / √x = 2 – √3



    Again,



    √x + 1 / √x = 2 + √3 + 2 – √3



    ⇒ √x + 1 / √x = 2 + 2



    ⇒ √x + 1 / √x = 4



    Hence,



    √x + 1 / √x = 4


    _______________________



    Thanks for the question!



    ☺️☺️☺️☺️





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    Blackqueen

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    TanishaDasila avatar

    It is helpfull


    Blackqueen avatar

    welcome!!☺️


    Hey @blackqueen can’t you plss unblock me 🙁


    Blackqueen avatar

    No!! m sorry!


    but can you plss tell me reason why can’t you? 🙁



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