Any way to solve parametric inequations?
09-13-2021, 09:33 PM (This post was last modified: 09-13-2021 09:36 PM by jte.)
Post: #8
 jte Member Posts: 145 Joined: Feb 2014
RE: Any way to solve parametric inequations?
(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)}
CAS> assume(y<0)
CAS> solve(x*y/(x+y)^2 ≤ 0, x) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → {(x≥0) AND (x<(-y)),x>(-y)}

Nice! It was fun seeing this … & trying it myself! Good for us to be reminded of the power and versatility of the CAS.

(Maybe some of my joy here, with this, was influenced by my difficulties in getting a government website to produce a QR code for me that wasn’t needlessly blurry. argh!)

(09-13-2021 07:42 PM)Albert Chan Wrote:  Or, for y≠0, …

… hmmm, yes… what about when y is zero (with the above)? Is a little touching-up appropriate?

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

CAS> solve(t/(t+1)^2 ≤ 0, t) ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ ﻿ → {t<-1,(t>-1) AND (t≤0)}
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 Messages In This Thread Any way to solve parametric inequations? - dah145 - 09-04-2021, 02:49 AM RE: Any way to solve parametric inequations? - jte - 09-05-2021, 04:30 PM RE: Any way to solve parametric inequations? - dah145 - 09-07-2021, 09:48 PM RE: Any way to solve parametric inequations? - jte - 09-12-2021, 11:42 PM RE: Any way to solve parametric inequations? - parisse - 09-13-2021, 04:49 PM RE: Any way to solve parametric inequations? - roadrunner - 09-13-2021, 06:39 PM RE: Any way to solve parametric inequations? - Albert Chan - 09-13-2021, 07:42 PM RE: Any way to solve parametric inequations? - jte - 09-13-2021 09:33 PM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021, 12:55 AM RE: Any way to solve parametric inequations? - jte - 09-14-2021, 05:13 AM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021, 09:35 AM RE: Any way to solve parametric inequations? - Albert Chan - 09-14-2021, 10:23 AM RE: Any way to solve parametric inequations? - jte - 09-14-2021, 10:58 PM RE: Any way to solve parametric inequations? - parisse - 09-15-2021, 04:53 AM

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