Any way to solve parametric inequations?

[jte]

(09-14-2021 12:55 AM)Albert Chan Wrote:  

(09-13-2021 07:42 PM)Albert Chan Wrote:  Or, for y≠0, reduce to simple inequality, with t = x/y

CAS> solve(t/(t+1)^2 ≤ 0, t)            → {t<-1,(t>-1) AND (t≤0)}

(09-13-2021 09:33 PM)jte Wrote:  … hmmm, yes… what about when y is zero (with the above)? Is a little touching-up appropriate?

Oh! Now I see that I wasn’t clear with “with the above” (sorry about that!); by that I meant all the way up to the x,y solution for non-negative y (this is why I cut into the post mid-sentence, so that t’s introduction would be below rather than above); or, in other words, up to the following:

(09-13-2021 07:42 PM)Albert Chan Wrote:  ⋮
CAS> assume(y≥0)
CAS> solve(x*y/(x+y)^2 ≤ 0, x)       → {x<(-y),(x>(-y)) AND (x≤0)}
⋮

(It seems to me that the x>0,y=0 portion is missing.)

(09-14-2021 12:55 AM)Albert Chan Wrote:  ⋮
Even with some edge cases, I still prefer dimensionless solution

Yes — I’m glad my getting another chance to write lets me express my appreciation for seeing the t=x/y approach (or t=y/x)! I enjoyed imagining a line going through the origin with the slope varying, and thinking how that related to the problem (and your given solution set for t).