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# Dear sir pls ans this inequality question not by squaring both sides as doesn't work out always.|x^2-2x|+|x-4|>|x^2-3x+4|Thanks

Arun Kumar IIT Delhi
askIITians Faculty 256 Points
7 years ago
Hi Jai,
$See \\|x^2-2x|+|x-4|>|x^2-3x+4| \\=>|x^2-2x|+|4-x|>|x^2-3x+4|$
if you sum the things between modes they are equal.
So by triangle
they all should be positive or all negative but that we don't have to do.
So on of them should be negative.
$A=x^2-2x \\=>B=4-x \\=>C=x^2-3x+4 \\1-A>0,B>0,C<0 \\2-A>0,B<0,C>0 \\3-A<0,B>0,C>0 \\4-A<0,B<0,C>0 \\5-A<0,B>0,C<0 \\6-A>0,B<0,C<0$
6 case only few of them will generate common interval for x.

Thanks & Regards
Arun Kumar
IIT Delhi