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mukushla
Group Title
ok this is mine
\[f(x)=\sqrt[3]{x1}+\sqrt[3]{3x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
 2 years ago
 2 years ago
mukushla Group Title
ok this is mine \[f(x)=\sqrt[3]{x1}+\sqrt[3]{3x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
 2 years ago
 2 years ago

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sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
f(x)=2 and 1
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
@nipunmalhotra93 @sauravshakya post complete solution ... i'll check it later
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Take it to the form a^3+b^3
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
dw:1347716779899:dw
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Wll that be enough
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
So, f(x) can only be either 1 or 2
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
So the hard part is to find x
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Was that correct @mukushla
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
thats correct...complete it :) can u find the exact range of f(x) ?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
dw:1347720322437:dw
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
well, here's my solution. dw:1347734655828:dwdw:1347734803553:dw
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
dw:1347736319687:dw
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
dw:1347736404280:dw
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
so three answers in total.... :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
Fantastic work @nipunmalhotra93 :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
i think the answer is only x=2
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
dw:1347769714174:dw
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
I think that also works
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
that gives f(x)=1 ?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
And is solved the equation
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
emm... http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7Bx1%7D%2B%5Csqrt%5B3%5D%7B3x%7D%3D1
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
WHAT! so my solution was wrong
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
because the range of that function is\[[\sqrt[3]{2},2]\]
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Cant it be zero as x>infinity
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Oh I got it there is a problem with my solution
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
So if (x)^1/2 + y^1/2 =2........i and x^1/2  y^1/2 =4.......ii
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
It has no solution........ though we get the value of x and y..... if we solve those equation
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Same thing happened to my equations
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
right? @mukushla
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
where that equations come from?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Actually the equations I got was: (x1)^1/3  (x3)^1/3 =1...........i (x1)^2/3 +{(x1)(x3)}^1/3 + (x3)^2/3=2........ii
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Solved those two equations
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Let x1=A and x3=B
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Square first equation
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
dw:1347770764883:dw
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
@mukushla actually I think that wolfram uses the domain of \[\sqrt[3]{x}\]to be only non negative real nos. I have noticed that it gives complex answers when we try to plug in negative reals in the cube root function http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7B1%7D
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
yeah thats right...have u checked ur solutions?
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
yup! when I plug in x=.98165, calculate cube root of 1x and then put a minus sign with it. That works fine.
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
similarly, when I put x=3.0183 , I calculate x3 and put minus sig with the cube root of x3 to get \[\sqrt[3]{3x}\] That's the only possible way to check it I think.
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
@nipunmalhotra93 Actually u and I got the same answers....dw:1347775568533:dw But And the substituted the value dw:1347775753579:dw in f(x) I got 1
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
@mukushla can u PLZ CHECK it
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
I think the range of f(x) isdw:1347775870157:dw
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
thats right :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
good job saura :)
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
But I still have a question for u
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
guys @sauravshakya @nipunmalhotra93 u cooked the problem :D
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
yeah what ?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
(x1)^1/3  (x3)^1/3 =1...........i (x1)^2/3 +{(x1)(x3)}^1/3 + (x3)^2/3=2........ii
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
There I solved for x and got the value
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Similarly if I solved this (x)^1/2 + y^1/2 =2........i and x^1/2  y^1/2 =4.......ii
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Will I get the values of x and y
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
sorry can u plz elaborate ? where these 2 equations come from?
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Which one: (x1)^1/3  (x3)^1/3 =1...........i (x1)^2/3 +{(x1)(x3)}^1/3 + (x3)^2/3=2........ii
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
this one
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Second one just came from my mind
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
While I gave a thought when u said that x=2 only
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
nope there is no answer for that system
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
that gives\[\sqrt{y}=1\]
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
So, Actually my approach was not really good............ As it may give somrtime solution when there should be no solution
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
yeah maybe :)
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
ok i really enjoyed guys....thank u
 2 years ago

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Welcome........ And thanx for such a nice question
 2 years ago

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
@sauravshakya haha yea we both had the same answer :D @mukushla I enjoyed it too man... thanks !!
 2 years ago
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