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Math Help - indices

  1. #1
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    indices

    if  a=2^x+2^{-x}, and b=2^x-2^{-x}, find an expression for a^2+b^2
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  2. #2
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    Hello, requal!

    Did you do the algebra?


    If  a\,=\,2^x+2^{-x} and b\,=\,2^x-2^{-x}, find an expression for a^2+b^2

    . . a^2 \:=\:\left(2^x + 2^{-x}\right)^2 \:=\:(2^x)^2 + 2(2^x)(2^{-x}) + (2^{-x})^2 \:=\:2^{2x} + 2 + 2^{-2x} .[1]

    . . b^2 \:=\:\left(2^x-2^{-x}\right)^2 \:=\:(2^x)^2 - 2(2^x)(2^{-x}) + (2^{-x})^2 \:=\:2^{2x} - 2 + 2^{-2x} .[2]


    Add [1] and [2]: . a^2+b^2 \;=\;2\cdot2^{2x} + 2\cdot2^{-2x} \;=\;2^{2x+1} + 2^{-2x+1}

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