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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3Actually 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

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

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

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

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

nipunmalhotra93
 2 years ago
Best 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

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

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

nipunmalhotra93
 2 years ago
Best ResponseYou've already chosen the best response.1similarly, 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.

sauravshakya
 2 years ago
Best 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

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

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

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

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

sauravshakya
 2 years ago
Best 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

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

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

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

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

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

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

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

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

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

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

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

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

nipunmalhotra93
 2 years ago
Best 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 !!
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