incorrect answer from solve() solving inequality

07022019, 08:21 AM
Post: #1




incorrect answer from solve() solving inequality  
07022019, 08:58 AM
Post: #2




RE: incorrect answer from solve() solving inequality  
07022019, 02:32 PM
(This post was last modified: 07022019 02:32 PM by parisse.)
Post: #3




RE: incorrect answer from solve() solving inequality
Even if x is negative, the expression 1/(x+sqrt(x))+1/(xsqrt(x)) is real valued :
normal(1/(x+sqrt(x))+1/(xsqrt(x))) returns 2/(x1) Therefore the Prime answer is correct, and x=0 is also valid (since the limit at x=0 is 2 and 2<=1). 

07022019, 04:46 PM
Post: #4




RE: incorrect answer from solve() solving inequality
Thank you, parisse.
For x is negative, it means that each of 1/(x+sqrt(x)), 1/(xsqrt(x)) to be complex number. If so, that is correct. For x is zero, (1/(x+sqrt(x))+1/(xsqrt(x))) = (xsqrt(x) + x + sqrt(x))/(x^2x) = (2x)/(x*(x1)) and this will be equal to 2/(x1) if x<> 0 (otherwise, it will be 0/0) So (1/(x+sqrt(x))+1/(xsqrt(x))) when x=0 should be undefined. However, lim x>0 of (1/(x+sqrt(x))+1/(xsqrt(x))) is 2. 

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