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Math Help - If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?

  1. #1
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    If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?

    Can any kind soul help me in the below?
    Please assist in (b)

    a) Factorise t^4 - 16
    b) If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?
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  2. #2
    Super Member Bacterius's Avatar
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    Well, a) is easy, if you note that 16 = 4^2 (or 2^4).

    Second question : I guess there is another more clever way to do this but I would have solved for x first, then evaluated.

    Since (x + \frac{2}{x})^2 = 36, we have x + \frac{2}{x} = 6, thus \frac{x^2}{x} + \frac{2}{x} = 6, therefore \frac{x^2 + 2}{x} = 6, so x^2 + 2 = 6x, and so, x^2 - 6x + 2 = 0.

    By means of the quadratic formula (for example), you find that x equals that value and that value, then you substitute your results back into the second equation and evaluate.

    Does that make sense ?
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  3. #3
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    Dear Bacterius, thanks so much!! but i cannot get the answer of 32.
    The topic is solving quadratic equations by factorisation.
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  4. #4
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    Quote Originally Posted by ppppp77 View Post
    Can any kind soul help me in the below?
    Please assist in (b)

    a) Factorise t^4 - 16


    Remember that a^2-b^2=(a-b)(a+b) , so in this case substitute a=t^2\,,\,\,b=4 ...


    b) If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?
    We have that \left(\frac{x+2}{x}\right)^2=36\Longrightarrow \frac{x+2}{x}=\pm 6\Longrightarrow ....get the two possible values for x and substitute.

    Tonio
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  5. #5
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    Krizalid's Avatar
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    Quote Originally Posted by ppppp77 View Post
    b) If (x + 2/x)^2 = 36, then what is (x^2 + 2/x^2)^2?
    wonder if in the second expression it's actually a \frac4{x^2} instead of the \frac2{x^2}, because \left( x^{2}+\frac{4}{x^{2}} \right)^{2}=\left( \left( x+\frac{2}{x} \right)^{2}-4 \right)^{2}=32^{2}.
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  6. #6
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    Thanks so much Krizalid! I thought the same too.
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