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System for which Solve and NSolve both fail

  • To: mathgroup at smc.vnet.net
  • Subject: [mg30572] System for which Solve and NSolve both fail
  • From: Ben Langton <ben at spam.bugs.me.quickmath.com>
  • Date: Wed, 29 Aug 2001 01:40:17 -0400 (EDT)
  • Organization: OzEmail Ltd, Australia
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I noticed that Mathematica seems unable to solve this system of equations :

3^x + 3^y = 90

x + y = 6

With a bit of thought, you can see by inspection that the solutions are

{x , y} = {2 , 4} or {4 , 2}

However, when I use the commands

Solve[{3^x+3^y==90,x+y==6},{x,y}]

or

NSolve[{3^x+3^y==90,x+y==6},{x,y}]

I get a warning message starting with

Solve::incnst: Inconsistent or redundant transcendental equation

Can anyone shed some light on what is going on here? Any way to get around
this problem?

(I am using Mathematica v 3.0.0.0 under Mac OS 9.2.1, although I believe a
similar thing occurs under v 4.x)

Regards,

Ben Langton

http://www.quickmath.com/


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