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anonymous

  • one year ago

x+1/x+2=6 is given. Find (x+2)^2+1/(x+2)^2.

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  1. DanJS
    • one year ago
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    \[\frac{ x+1 }{ x+2 } = 6\]

  2. DanJS
    • one year ago
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    that right?

  3. DanJS
    • one year ago
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    (x+1)/(x+2) = 6

  4. anonymous
    • one year ago
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    \[x+\frac{ 1 }{x+2 }=6, (x+2)^2+\frac{ 1 }{ (x+2)^{2}}=?\]

  5. DanJS
    • one year ago
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    solve the equation for x, then use that x in the expression to find a value

  6. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & x+2+\frac{ 1 }{x+2 }=8, \hspace{.33em}\\~\\ \end{align}}\)

  7. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & put\ \ x+2=a \hspace{.33em}\\~\\ \end{align}}\)

  8. anonymous
    • one year ago
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    ok thank you i could not think i should add 2 to both sides so the answer is 62

  9. mathmath333
    • one year ago
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    ans square both sides

  10. ganeshie8
    • one year ago
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    that is clever! \(a+\frac{1}{a} = k \implies a^2+\frac{1}{a^2} = k^2-2\)

  11. DanJS
    • one year ago
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    yeah, looks like that was the point of the problem.. nice

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