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ok this is mine
\[f(x)=\sqrt[3]{x1}+\sqrt[3]{3x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
 one year ago
 one year ago
ok this is mine \[f(x)=\sqrt[3]{x1}+\sqrt[3]{3x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
 one year ago
 one year ago

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mukushlaBest ResponseYou've already chosen the best response.1
@nipunmalhotra93 @sauravshakya post complete solution ... i'll check it later
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Take it to the form a^3+b^3
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
dw:1347716779899:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Wll that be enough
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
So, f(x) can only be either 1 or 2
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
So the hard part is to find x
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Was that correct @mukushla
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
thats correct...complete it :) can u find the exact range of f(x) ?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
dw:1347720322437:dw
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
well, here's my solution. dw:1347734655828:dwdw:1347734803553:dw
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
dw:1347736319687:dw
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
dw:1347736404280:dw
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
so three answers in total.... :)
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
Fantastic work @nipunmalhotra93 :)
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
i think the answer is only x=2
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
dw:1347769714174:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
I think that also works
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
And is solved the equation
 one year ago

mukushlaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
WHAT! so my solution was wrong
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
because the range of that function is\[[\sqrt[3]{2},2]\]
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Cant it be zero as x>infinity
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Oh I got it there is a problem with my solution
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Same thing happened to my equations
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
where that equations come from?
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Solved those two equations
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Let x1=A and x3=B
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Square first equation
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
dw:1347770764883:dw
 one year ago

nipunmalhotra93Best 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
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
yeah thats right...have u checked ur solutions?
 one year ago

nipunmalhotra93Best 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.
 one year ago

nipunmalhotra93Best 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.
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
@mukushla can u PLZ CHECK it
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
I think the range of f(x) isdw:1347775870157:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
But I still have a question for u
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
guys @sauravshakya @nipunmalhotra93 u cooked the problem :D
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
There I solved for x and got the value
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Will I get the values of x and y
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
sorry can u plz elaborate ? where these 2 equations come from?
 one year ago

sauravshakyaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Second one just came from my mind
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
While I gave a thought when u said that x=2 only
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
nope there is no answer for that system
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
that gives\[\sqrt{y}=1\]
 one year ago

sauravshakyaBest 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
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
ok i really enjoyed guys....thank u
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Welcome........ And thanx for such a nice question
 one year ago

nipunmalhotra93Best 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 !!
 one year ago
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