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April 15th, 2017, 01:20 PM  #1 
Newbie Joined: Apr 2017 From: brazil Posts: 4 Thanks: 0  Irrational Inequation, how does one solve this?
x + (x210x+9)^(1/3) > [x+2(x210x+9)^(1/2)]^(1/2) Solution: 45/4 < x < 1 or x >= 9 Last edited by skipjack; April 17th, 2017 at 02:54 AM. 
April 16th, 2017, 01:09 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
Is there a typing error? The solution given is incorrect, as can be verified by substituting x = 0.

April 16th, 2017, 09:58 AM  #3 
Newbie Joined: Apr 2017 From: brazil Posts: 4 Thanks: 0 
not sure, I don't even know what to do with it. It must be an error, but still, how do I solve the question then?

April 16th, 2017, 03:04 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
Where did you get the question from? It appears that x + (x²  10x + 9)^(1/2) > [x + 2(x²  10x + 9)^(1/2)]^(1/2) was intended. 
April 16th, 2017, 04:21 PM  #5 
Newbie Joined: Apr 2017 From: brazil Posts: 4 Thanks: 0 
can no one solve this question ?

April 16th, 2017, 05:33 PM  #6 
Newbie Joined: Apr 2017 From: brazil Posts: 4 Thanks: 0 
thank you guys!

April 17th, 2017, 03:01 AM  #7 
Global Moderator Joined: Dec 2006 Posts: 18,954 Thanks: 1601 
Consider x + √(x²  10x + 9) = √(x + 2√(x²  10x + 9)). Squaring both sides gives 2x²  10x + 9 + 2x√(x²  10x + 9) = x + 2√(x²  10x + 9). Rearranging that gives 2x²  11x + 9 = 2√(x²  10x + 9)  2x√(x²  10x + 9), i.e., (x  1)(2x  9) = 2(x  1)√(x²  10x + 9). Hence x = 1 or 2x  9 = 2√(x²  10x + 9). Squaring that gives (2x  9)² = 4(x²  10x + 9), i.e. 4x = 45, so x = 45/4. Solving the intended original inequation is now straightforward. 

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inequation, irracional, irrational, solve 
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