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March 10th, 2013, 08:51 PM  #1 
Member Joined: Sep 2012 Posts: 69 Thanks: 0  proof involving real number!
Question Let x be a positive real number. Prove that if , then . (a) a direct proof Assume is true. Then, Since and , is positive real number. If x is less than or equal to 2, then . Therefore, . Q.E.D Any comment?? And can anyone prove this by contrapositive?? Thanks. 
March 10th, 2013, 10:30 PM  #2 
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  Re: proof involving real number!
Correct. Maybe you should have stated the reason for x(x2)<=2. Anyway. x^2x = (x1/2)^2  1/4 you can wtite (x1/2)^2 > 9/4 i.e. x>2 As we can see the (in)equality x2/x ? 1 is logically the same than x ? 2. 
March 12th, 2013, 03:41 PM  #3 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: proof involving real number!
Contrapositive: If then so .


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