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mathmath333

  • one year ago

fun question

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  1. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} &\text{if}\quad p,q,r \quad \text{are roots of } \hspace{.33em}\\~\\ &x^3-5x-4=0 \hspace{.33em}\\~\\ &\text{find }\quad \left(\dfrac{1}{p+q}+\dfrac{1}{r+q}+\dfrac{1}{p+r}\right) \end{align}}\)

  2. imqwerty
    • one year ago
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    5/4

  3. mathmath333
    • one year ago
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    that's correct!

  4. anonymous
    • one year ago
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    yeah 5/4

  5. mathmath333
    • one year ago
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    by the way how did u find that

  6. imqwerty
    • one year ago
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    sorry for the cuttings

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  7. ganeshie8
    • one year ago
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    \[x^3-5x-4=0\] Vieta's formulas gives sum of roots : \(p+q+r=0 \implies p+q=-r, ~q+r=-p,~~r+p=-q\) \(pq+qr+rp=-5\) \(pqr=4\) plugging them in the given expression we get \[\begin{align}& \frac{1}{-r}+\frac{1}{-p}+\frac{1}{-q}\\~\\&=-\frac{pq+qr+rp}{pqr}\\~\\&=-\frac{-5}{4}\end{align}\]

  8. imqwerty
    • one year ago
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    damn i didn't thought that way

  9. skullpatrol
    • one year ago
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    you have two minus signs in your answer @ganeshie8

  10. ganeshie8
    • one year ago
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    Haha final answer is indeed +5/4

  11. skullpatrol
    • one year ago
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    :D

  12. mathmath333
    • one year ago
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    that was the actual way

  13. skullpatrol
    • one year ago
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    what do you mean by "actual"?

  14. mathmath333
    • one year ago
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    efficient , optimal

  15. skullpatrol
    • one year ago
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    Is there such a thing as an "efficient" or "optimal" way to have fun with a question in math?

  16. ganeshie8
    • one year ago
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    I think many times there exists "the" best way to solve a problem... initially i tried combining the fractions and expanding everything but that went v messy it actually took some time to see that p+q+r=0 is useful

  17. imqwerty
    • one year ago
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    that's what makes u the professor :)

  18. mathmath333
    • one year ago
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    @skullpatrol using the fact p+q+r=0 makes it easy , while trying to solve it with rigour loos like to kill a rat with atom bomb that's why it was fun question

  19. ParthKohli
    • one year ago
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    @parthkohli. holy hell, haha, who's this

  20. skullpatrol
    • one year ago
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    Thank you for making the intent of your objective clear :-)

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