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anonymous
 3 years ago
ok this is mine
\[f(x)=\sqrt[3]{x1}+\sqrt[3]{3x}\]find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
anonymous
 3 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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anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@nipunmalhotra93 @sauravshakya post complete solution ... i'll check it later

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Take it to the form a^3+b^3

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1347716779899:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So, f(x) can only be either 1 or 2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So the hard part is to find x

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Was that correct @mukushla

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0thats correct...complete it :) can u find the exact range of f(x) ?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1347720322437:dw

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

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

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Fantastic work @nipunmalhotra93 :)

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0i think the answer is only x=2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1347769714174:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I think that also works

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0And is solved the equation

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0emm... http://www.wolframalpha.com/input/?i=%5Csqrt%5B3%5D%7Bx1%7D%2B%5Csqrt%5B3%5D%7B3x%7D%3D1

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0WHAT! so my solution was wrong

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0because the range of that function is\[[\sqrt[3]{2},2]\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Cant it be zero as x>infinity

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Oh I got it there is a problem with my solution

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So if (x)^1/2 + y^1/2 =2........i and x^1/2  y^1/2 =4.......ii

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0It has no solution........ though we get the value of x and y..... if we solve those equation

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Same thing happened to my equations

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0where that equations come from?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Actually 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Solved those two equations

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Square first equation

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1347770764883:dw

nipunmalhotra93
 3 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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yeah thats right...have u checked ur solutions?

nipunmalhotra93
 3 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
 3 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0@mukushla can u PLZ CHECK it

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I think the range of f(x) isdw:1347775870157:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0But I still have a question for u

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0guys @sauravshakya @nipunmalhotra93 u cooked the problem :D

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0(x1)^1/3  (x3)^1/3 =1...........i (x1)^2/3 +{(x1)(x3)}^1/3 + (x3)^2/3=2........ii

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0There I solved for x and got the value

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Similarly if I solved this (x)^1/2 + y^1/2 =2........i and x^1/2  y^1/2 =4.......ii

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Will I get the values of x and y

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0sorry can u plz elaborate ? where these 2 equations come from?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Which one: (x1)^1/3  (x3)^1/3 =1...........i (x1)^2/3 +{(x1)(x3)}^1/3 + (x3)^2/3=2........ii

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Second one just came from my mind

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0While I gave a thought when u said that x=2 only

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0nope there is no answer for that system

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0that gives\[\sqrt{y}=1\]

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0So, Actually my approach was not really good............ As it may give somrtime solution when there should be no solution

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0ok i really enjoyed guys....thank u

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0Welcome........ And thanx for such a nice question

nipunmalhotra93
 3 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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