Show that 8 − 4 3 12 3 − 20 3 = 2 1 6 This was the result of evaluating an integral by two different methods. The RHS was obtained by making a substitution, the LHS was obtained using trigonometric identity's and partial fractions.Now I know that these two are equal, but I just can't prove it. I tried writing the LHS in terms of powers of 2, but can't get any further to the desired result.

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Show that                     8        −        4                  3                                      12                      3                    −          20                3              =      2          1      6      This was the result of evaluating an integral by two different methods. The RHS was obtained by making a substitution, the LHS was obtained using trigonometric identity&#039;s and partial fractions.Now I know that these two are equal, but I just can&#039;t prove it. I tried writing the LHS in terms of powers of 2, but can&#039;t get any further to the desired result.

Terrance Phillips · Accepted Answer

We have  8  −  4      3    =  2  (  4  −  2      3    )  =  2  (  3  −  2      3    +  1  )  =  2  (      3    −  1      )    2    ,so       8    −    4          3        =      2    (      3    −  1  )Then we see that looking at   (      3    −  1      )    3    is a good idea:  (      3    −  1      )    3    =  (  4  −  2      3    )  (      3    −  1  )  =  6      3    −  10  , so   12      3    −  20  =  2  (      3    −  1      )    3   and             12              3            −      20        3    =      2    3    (      3    −  1  )            2              2      3        =      2          1              /            6       is then easy to see.

Briana Petty · Accepted Answer

8      −      4              3                            12                  3                −        20            3        =                              4          3                (        2        −                  3                          )          3                                      4          2                (        3                  3                −        5                  )          2                      6    =                    4        (        2        −                  3                          )          3                            (        3                  3                −        5                  )          2                      6    =                    4        (        8        −        12                  3                +        18        −        3                  3                )                    (        27        −        30                  3                +        25        )              6    =                    4        (        26        −        15                  3                )                    (        52        −        30                  3                )              6    =                    4        (        26        −        15                  3                )                    2        (        26        −        15                  3                )              6    =      2                  1        6

Show that <mstyle displaystyle="true" scriptlevel="0"> <msqrt> 8

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