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mathmath333
 one year ago
fun question
mathmath333
 one year ago
fun question

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2\(\large \color{black}{\begin{align} &\text{if}\quad p,q,r \quad \text{are roots of } \hspace{.33em}\\~\\ &x^35x4=0 \hspace{.33em}\\~\\ &\text{find }\quad \left(\dfrac{1}{p+q}+\dfrac{1}{r+q}+\dfrac{1}{p+r}\right) \end{align}}\)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2by the way how did u find that

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3sorry for the cuttings

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[x^35x4=0\] 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 \[\begin{align}& \frac{1}{r}+\frac{1}{p}+\frac{1}{q}\\~\\&=\frac{pq+qr+rp}{pqr}\\~\\&=\frac{5}{4}\end{align}\]

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3damn i didn't thought that way

skullpatrol
 one year ago
Best ResponseYou've already chosen the best response.0you have two minus signs in your answer @ganeshie8

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1Haha final answer is indeed +5/4

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2that was the actual way

skullpatrol
 one year ago
Best ResponseYou've already chosen the best response.0what do you mean by "actual"?

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2efficient , optimal

skullpatrol
 one year ago
Best ResponseYou've already chosen the best response.0Is there such a thing as an "efficient" or "optimal" way to have fun with a question in math?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1I 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

imqwerty
 one year ago
Best ResponseYou've already chosen the best response.3that's what makes u the professor :)

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.2@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

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.1@parthkohli. holy hell, haha, who's this

skullpatrol
 one year ago
Best ResponseYou've already chosen the best response.0Thank you for making the intent of your objective clear :)
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