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Math Help - If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

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    If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

    If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

    Sorry, I haven't gotten used to LaTex yet, so I'll be posting an image again:

    If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?-math-prob-2.png


    My answer is 100, but the book says 98. How do you solve this?

    Thank you!
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    Re: If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

    Quote Originally Posted by viccal View Post
    If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

    Sorry, I haven't gotten used to LaTex yet, so I'll be posting an image again:

    Click image for larger version. 

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    My answer is 100, but the book says 98. How do you solve this?

    Thank you!
    \displaystyle \begin{align*} 4x + \frac{4}{x} &= 40 \\ x + \frac{1}{x} &= 10 \\ \left(x + \frac{1}{x}\right)^2 &= 10^2 \\ x^2 + 2 + \frac{1}{x^2} &= 100 \\ x^2 + \frac{1}{x^2} &= 98 \end{align*}
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    Re: If 4x + 4/x = 40, what is the value of x^2 + 1/x^2?

    Oh, wow! Thanks a lot! I didn't realize how careless I was in solving it. Thanks!
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