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kshitij's latest activity
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I didn't knew there were multiple winning strategies for ##P##! Also, couldn't we generalise that further for when ##P## chooses any...
Jul 3, 2021
kshitij
reacted to
fresh_42's post
in the thread
Challenge
Math Challenge - July 2021
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Like
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Ok, I finally got it. It took so long and several posts that I post my solution as reference: ##P## has the following winning strategy...
Jul 3, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
When I first used ##A.M \geq G.M## on$$f(x,y,z)=c(c-2x)(c-2y)(c-2z)$$ the equality would never hold because if $$c=c-2x=c-2y=c-2z$$ then...
Jul 3, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
So, basically as I understand it, we had $$f(x,y,z)=c(c-2x)(c-2y)(c-2z)$$ And ##c## is a constant, so we use ##A.M \geq G.M## on...
Jul 3, 2021
kshitij
reacted to
fresh_42's post
in the thread
Challenge
Math Challenge - July 2021
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I am saying that any upper bound is not sufficient. We are looking for the maximum. We get from your calculation and the fact that...
Jul 3, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
Also I forgot that ##x,y,z \gt 0## so ##x=y=z=0## cannot be correct anyway. I will try again this problem later.
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
But if ##f(x,y,z)## is area of a triangle then ##f(x,y,z)=0## is the least possible value not the maximum value, surely this is wrong!
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
Are you saying that I must prove why the equality holds? or do you want me to show when the equality holds? As I said that for...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I think I have just a strategy but I am not sure because lets say that P plays according to my strategy and chooses a negative value of...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I just noticed that $$c(c-2x)(c-2y)(c-2z)$$ Looks similar to the formula for area of a triangle! Is that what you meant, is geometrical...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I don't know about why is that maximum, if equality holds then they should be maximum. I think I don't understand what you're trying to...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I don't understand what you're saying? How can the equation ##y=x^3+c## have three different real roots for any value of ##c##?
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
I might be wrong, but I thought that when ##a=0## then, if the value of ##b## is chosen to be positive, then the equation...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
But I applied ##A.M \geq G.M## on $$(z-x+y)(z+x-y)(x+y-z)(x+y+z)$$ ##(z-x+y),(z+x-y),(x+y-z)## and ##(x+y+z)## aren't necessarily...
Jul 2, 2021
kshitij
replied to the thread
Challenge
Math Challenge - July 2021
.
You can ignore this attempt, as the question doesn't say that ##x,y,z\gt 0## so we cannot use ##A.M \geq G.M##
Jul 2, 2021
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