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 2 years ago
dont need weird mathematics :)
\[f(x)=\sqrt{x^22x+10}\sqrt{x^22x+2}\]
find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
 2 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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mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1@sauravshakya @ganeshie8 @eliassaab @TuringTest

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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1u are close :) but dont tell the answer plz...so others can think on that :)

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3So only when x=1 or are there any other value..... I think yes because irrationalirrational can be integer

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3I mean are there any other values of x

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1dont post ur solution :) just values of x

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3So I delete it and send u msg for the vaues of x

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1no give the values of x here :)

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3dw:1347712962196:dw

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3So was my answer correct @nipunmalhotra93

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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1so i think nipun got it also :)

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3Took me a lot to do this......

nipunmalhotra93
 2 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

mukushla
 2 years ago
Best ResponseYou've already chosen the best response.1everyone is one here...lol

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3@mukushla CAN U PLZ GIVE SOME QUESTION LIKE THIS PLZ.......

nipunmalhotra93
 2 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. :)

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3Rationalize and u will getdw:1347715001113:dw

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3That will make it easy to solve

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

sauravshakya
 2 years ago
Best ResponseYou've already chosen the best response.3So, 2*(x^22x+10)^1/2=9
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