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How do I solve an equation for a power of $t$, e.g. solving $$-t(x–8)/8 = –2(x+4)/t$$ for $t^2$ instead of $t$, i.e. to get the answer $$t^2=16(x+4)/(x–8)$$ from Solve?

I can solve it for $t$ easily and square $t$, but can it be done 'directly' using Solve? TIA.

mf67
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  • Have you read the documentation pages of Solve? – Artes Feb 13 '20 at 14:27
  • Yes, but probably not every paragraph. Perhaps you can point the section which answers my question. I cannot find any suitable example in the text. – mf67 Feb 13 '20 at 14:32
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    Solve[{-t(x-8)/8==-2(x+4)/t, t^2==16(x+4)/(x-8)}, x] should work, in case of doubts read this post What is the difference between Reduce and Solve? – Artes Feb 13 '20 at 14:37
  • Solve[-t (x - 8)/8 == -2 (x + 4)/t, x] yields x -> (8 (8 + t^2))/(-16 + t^2). Is it what you want? – Alexei Boulbitch Feb 13 '20 at 15:05
  • A small misunderstand due to my poor initial description. What I meant to ask was how to solve an equation with respect to t^p, e.g. t^2, and not t. Thus I would like to have ´Solve´ reply with the right hand side of t^2 = ... and not t = square root something. I hope this made it more clear. – mf67 Feb 13 '20 at 15:08

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sol = Solve[-t (x - 8)/8 == -2 (x + 4)/t /. t -> Sqrt[tt], tt] /. tt -> t^2

(*   {{t^2 -> (16 (4 + x))/(-8 + x)}}   *)

Equal @@ (First@First@sol)

(*   t^2 == (16 (4 + x))/(-8 + x)   *)

Or

Reduce[-t (x - 8)/8 == -2 (x + 4)/t /. t -> Sqrt[tt], tt] /. tt -> t^2

(*   -8 + x != 0 && 4 + x != 0 && t^2 == (16 (4 + x))/(-8 + x)   *)
Akku14
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