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

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mukushlaBest ResponseYou've already chosen the best response.1
@sauravshakya @ganeshie8 @eliassaab @TuringTest
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
x=1,\[\frac{ 1\sqrt{5} }{2 }\], \[\frac{1+\sqrt{5} }{2 }\]
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
u are close :) but dont tell the answer plz...so others can think on that :)
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
Ok fine. Thanks :)
 one year ago

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

sauravshakyaBest ResponseYou've already chosen the best response.3
I mean are there any other values of x
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
dont post ur solution :) just values of x
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
So I delete it and send u msg for the vaues of x
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
no give the values of x here :)
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
dw:1347712962196:dw
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
oh crap! I misread x^2 as x^3 :\
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
So was my answer correct @nipunmalhotra93
 one year ago

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

mukushlaBest ResponseYou've already chosen the best response.1
so i think nipun got it also :)
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Actually f(x)=2 and 1
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Took me a lot to do this......
 one year ago

nipunmalhotra93Best ResponseYou've already chosen the best response.1
:D the font is too small I thought it was x^3 lol :D
 one year ago

mukushlaBest ResponseYou've already chosen the best response.1
everyone is one here...lol
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
@mukushla CAN U PLZ GIVE SOME QUESTION LIKE THIS PLZ.......
 one year ago

nipunmalhotra93Best 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. :)
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
Rationalize and u will getdw:1347715001113:dw
 one year ago

mukushlaBest 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
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
That will make it easy to solve
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.3
opps. 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
 one year ago

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