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Question

Solve the following inequality:
|x23x|+x2<0

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Solution

|x23x|+x2<0
|x23x|<2x
x23x>(2x) & x23x<2x
x25x+2>0 & x22x2<0
(x5+172)(x5172)>0
xϵ(,5172)(5+172,)
x22x2<0
(x2+232)(x2232)<0
(x1+3)(x13)<0
xϵ(13,1+3)
So, xϵϕ

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