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posted by  mikesol on 9/7/2008 2:28:45 PM  |  status: Closed  

Another simple math proof

Course Textbook Chapter Problem
Other A transition to advanced mathematics 6th edition N/A N/A
Question Details:
Use the technique of working backward from the desired conclusion to prove that

if x and y are positive real numbers, then



Where in the proof is it essential that x and y be positive?
Tags: Math, Other
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posted by WSAN on 9/7/2008 7:50:33 PM  |  status: Live
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mikesol's comment:
"I don't get where the (Sqrt(x) - Sqrt(y))^2 part comes from"
Response Details:
 if x and y both negitive then xy is positive. so, is meaning ful.
but x,y are negitive ==> x+y is negitive and  if  is considered as positive number, then the statement will be false.
so, keeping these two cases in view, we confirm that both x  and y must be positive for this relation
we know that
further, a square is non negitive.
so,  
SWAN
Tags: Math, Other
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posted by CHEMNATION! on 9/8/2008 4:03:45 AM  |  status: Live
Asker's Rating: Lifesaver   
mikesol's comment:
"Ah ok thanks"
Response Details:
 
is part of the process of working backwards.  It is simply using the relationship
 (a - b)(a-b) = a2 - 2ab + b2 = a2 + b2 - 2ab
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Tags: Math, Other
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