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12312007  #1 
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surd inequality
please help with it:
square root(x+2x^2)<square root(x^23x+2)+x Last edited by agripa; 01012008 at 10:23 AM.. 
01012008  #2 
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be careful
Square roots provide plenty of opportunities to make mistakes. So do inequalities.
There may be a much easier way that I don't see, but I would square. If 0<a<b, then a^2<b^2 Since x+2+x^2 = (x+1/2)^2 + 7/4 > 0 , you can square to get x^2+4x < 2xsqrt(x^23x+2) After that you have to consider cases (x<0, x>0, x=4, x>4, x<4, etc) and square again. Happy New Year! 
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