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anonymous
 4 years ago
dont need weird mathematics :)
\[f(x)=\sqrt{x^22x+10}\sqrt{x^22x+2}\]
find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
anonymous
 4 years ago
dont need weird mathematics :) \[f(x)=\sqrt{x^22x+10}\sqrt{x^22x+2}\] find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@sauravshakya @ganeshie8 @eliassaab @TuringTest

nipunmalhotra93
 4 years ago
Best ResponseYou've already chosen the best response.1x=1,\[\frac{ 1\sqrt{5} }{2 }\], \[\frac{1+\sqrt{5} }{2 }\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0u are close :) but dont tell the answer plz...so others can think on that :)

nipunmalhotra93
 4 years ago
Best ResponseYou've already chosen the best response.1Ok fine. Thanks :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So only when x=1 or are there any other value..... I think yes because irrationalirrational can be integer

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I mean are there any other values of x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dont post ur solution :) just values of x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So I delete it and send u msg for the vaues of x

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0no give the values of x here :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0dw:1347712962196:dw

nipunmalhotra93
 4 years ago
Best ResponseYou've already chosen the best response.1oh crap! I misread x^2 as x^3 :\

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So was my answer correct @nipunmalhotra93

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

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so i think nipun got it also :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Actually f(x)=2 and 1

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Took me a lot to do this......

nipunmalhotra93
 4 years ago
Best ResponseYou've already chosen the best response.1:D the font is too small I thought it was x^3 lol :D

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0everyone is one here...lol

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0@mukushla CAN U PLZ GIVE SOME QUESTION LIKE THIS PLZ.......

nipunmalhotra93
 4 years ago
Best ResponseYou've already chosen the best response.1@sauravshakya I'd like to know your approach. Would you mind telling it? This is how I got it. \[\sqrt{p+10}\sqrt{p+2}=A\] A is natural so, \[p+10=A ^{2}+p+2+2A \sqrt{p+2}\] \[10A^22=2A \sqrt{p+2}\] so, \[\frac{ 4}{A }\frac{ A }{ 2 }=\sqrt{p+2}\] So, A can only be 1 or 2 (as A is natural) for \[\sqrt{p+2}\] to be real. Put p=x^22x and solving \[\sqrt{p+2}=1 or \sqrt{p+2}=7/2\] , we get the answer. This is a good question that's why I wanna know your method. :)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Rationalize and u will getdw:1347715001113:dw

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[f(x)=\sqrt{x^22x+10}\sqrt{x^22x+2}=\frac{8}{\sqrt{x^22x+10}+\sqrt{x^22x+2}}\]\[f(x)=\frac{8}{\sqrt{(x1)^2+9}+\sqrt{(x1)^2+1}}\le\frac{8}{\sqrt{9}+\sqrt{1}}=2\]so f(x)=1 or 2 same as saura's method

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That will make it easy to solve

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0opps. Now, when f(x)=1 (x^22x+10)^1/2  (x^22x+2)^1/2=1........i (x^22x+10)^1/2 + (x^22x+2)^1/2=8........ii

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So, 2*(x^22x+10)^1/2=9
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