anonymous
  • anonymous
dont need weird mathematics :) \[f(x)=\sqrt{x^2-2x+10}-\sqrt{x^2-2x+2}\] find all \(x \in \mathbb{R}\) such that \(f(x) \in \mathbb{N}\)
Meta-math
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
@sauravshakya @ganeshie8 @eliassaab @TuringTest
nipunmalhotra93
  • nipunmalhotra93
x=1,\[\frac{ -1-\sqrt{5} }{2 }\], \[\frac{-1+\sqrt{5} }{2 }\]
nipunmalhotra93
  • nipunmalhotra93
is that it?

Looking for something else?

Not the answer you are looking for? Search for more explanations.

More answers

anonymous
  • anonymous
let me check it :)
anonymous
  • anonymous
u are close :) but dont tell the answer plz...so others can think on that :)
nipunmalhotra93
  • nipunmalhotra93
Ok fine. Thanks :)
anonymous
  • anonymous
So only when x=1 or are there any other value..... I think yes because irrational-irrational can be integer
anonymous
  • anonymous
some other values...
anonymous
  • anonymous
I mean are there any other values of x
anonymous
  • anonymous
yeah there are.
anonymous
  • anonymous
dont post ur solution :) just values of x
anonymous
  • anonymous
Ok
anonymous
  • anonymous
So I delete it and send u msg for the vaues of x
anonymous
  • anonymous
no give the values of x here :)
anonymous
  • anonymous
|dw:1347712962196:dw|
nipunmalhotra93
  • nipunmalhotra93
oh crap! I misread x^2 as x^3 :\
anonymous
  • anonymous
So was my answer correct @nipunmalhotra93
anonymous
  • anonymous
@mukushla can u PLZ CHECK MY ANSWER
anonymous
  • anonymous
completely right :)
anonymous
  • anonymous
so i think nipun got it also :)
anonymous
  • anonymous
Actually f(x)=2 and 1
anonymous
  • anonymous
yup
anonymous
  • anonymous
GREAT QUESTION
anonymous
  • anonymous
Took me a lot to do this......
nipunmalhotra93
  • nipunmalhotra93
:D the font is too small I thought it was x^3 lol :D
anonymous
  • anonymous
everyone is one here...lol
anonymous
  • anonymous
@mukushla CAN U PLZ GIVE SOME QUESTION LIKE THIS PLZ.......
anonymous
  • anonymous
of course
anonymous
  • anonymous
GREAT
nipunmalhotra93
  • nipunmalhotra93
@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, \[p+10=A ^{2}+p+2+2A \sqrt{p+2}\] \[10-A^2-2=2A \sqrt{p+2}\] 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^2-2x 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
  • anonymous
Rationalize and u will get|dw:1347715001113:dw|
anonymous
  • anonymous
Right?
anonymous
  • anonymous
\[f(x)=\sqrt{x^2-2x+10}-\sqrt{x^2-2x+2}=\frac{8}{\sqrt{x^2-2x+10}+\sqrt{x^2-2x+2}}\]\[f(x)=\frac{8}{\sqrt{(x-1)^2+9}+\sqrt{(x-1)^2+1}}\le\frac{8}{\sqrt{9}+\sqrt{1}}=2\]so f(x)=1 or 2 same as saura's method
anonymous
  • anonymous
That will make it easy to solve
anonymous
  • anonymous
opps. Now, when f(x)=1 (x^2-2x+10)^1/2 - (x^2-2x+2)^1/2=1........i (x^2-2x+10)^1/2 + (x^2-2x+2)^1/2=8........ii
anonymous
  • anonymous
So, 2*(x^2-2x+10)^1/2=9
anonymous
  • anonymous
now, solve for x
anonymous
  • anonymous
thats it

Looking for something else?

Not the answer you are looking for? Search for more explanations.