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June 4th, 2011, 01:33 AM  #1 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  Surds(need help)
1.Find the square root of surdic quantities 73 +40?3 =( ?x + ?y)^2 73+40?3 = x+y + 2?xy x+y=73 y=73x ..........(1) 2?xy=40?3 ?xy=20?3 xy=1200 ........(2) substitute (1) into (2) x(73x)=1200 73x^2  x^2 =1200 x^273x+1200=0 then i m stuck at here,i have problem in factorize it 2.Show that ?2x3  ?x+2 =3?x1 does not have any real root. I know how to solve but i dunno how to show it does not have any real root. 3. Show that ?10+2?2 is less than 6 . This is the provided solution (?10+2?2)^2 = 10+ 2^2(2)+2(2)?10x2 = 18 + 4?20 = 18 + ?16x20 = 18+ ?320 (?10 + 2?2)^2 < 18 + ?324 ( i don understand how ?320 become ?324 ) < 18+18 < 36 ?10 + 2?2 < 6 Thank you . 
June 4th, 2011, 01:51 AM  #2 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
3. ?10 + 2?2 < 6 is trivial. Square both sides and we get 18 + 8?5 < 36, i.e. ?5 < 9/4 = ?(81/16). ?5 = ?(80/16) < ?(81/16), hence ?5 < 9/4 is correct, i.e. 18 + 8?5 < 36 is correct. Therefore ?10 + 2?2 < 6 is correct. 
June 4th, 2011, 03:44 AM  #3 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 465 Math Focus: Calculus/ODEs  Re: Surds(need help)
1.) x = 25, y = 48 or x = 48, y = 25 2.) Use parentheses to clearly show what the radicands are. I will ASSUME: Neither of these roots are in the domain of the original equation. 
June 4th, 2011, 06:49 AM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: Surds(need help) Hello, hoyy1kolko! Quote:
You had the right idea! \,+\,2\sqrt{xy}\,+\,y" /> \:=\:0 \;\;\;\Rightarrow\;\;\;x \:=\:25,\:48 \;\;\;\Rightarrow\;\;\;y \:=\:48,\:25" />  
June 4th, 2011, 06:58 AM  #5 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  Re: Surds(need help)
Thank you very much,i still don understand the solution from johnny for question 3 ,i need more help. What is mean by trivial? and isn't he use comparison to solve the question? 
June 4th, 2011, 02:59 PM  #6 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
What I mean by trivial is ?10 + 2?2 ?< 6, in another words we don't know if the inequality is true. Afterwards I did some simple mathematics to see that if it's true and then arrived at the correct conclusion. 
June 5th, 2011, 05:16 AM  #7 
Senior Member Joined: Dec 2010 Posts: 233 Thanks: 0  Re: Surds(need help)
Thank you very much!!!!!


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