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mukushla
Group Title
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
 2 years ago
mukushla Group Title
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
 2 years ago

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mukushla Group TitleBest ResponseYou've already chosen the best response.1
@sauravshakya @ganeshie8 @eliassaab @TuringTest
 2 years ago

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

nipunmalhotra93 Group TitleBest ResponseYou've already chosen the best response.1
is that it?
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
let me check it :)
 2 years ago

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

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

sauravshakya Group TitleBest 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
 2 years ago

mukushla Group TitleBest ResponseYou've already chosen the best response.1
some other values...
 2 years ago

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

mukushla Group TitleBest ResponseYou've already chosen the best response.1
yeah there are.
 2 years ago

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

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

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

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

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

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

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

mukushla Group TitleBest ResponseYou've already chosen the best response.1
completely right :)
 2 years ago

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

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

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
GREAT QUESTION
 2 years ago

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

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

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

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

nipunmalhotra93 Group TitleBest 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. :)
 2 years ago

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

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
Right?
 2 years ago

mukushla Group TitleBest 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
 2 years ago

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

sauravshakya Group TitleBest 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
 2 years ago

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

sauravshakya Group TitleBest ResponseYou've already chosen the best response.3
now, solve for x
 2 years ago
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