Re: Find the value of x & y
- To: mathgroup at smc.vnet.net
- Subject: [mg127832] Re: Find the value of x & y
- From: Bob Hanlon <hanlonr357 at gmail.com>
- Date: Sat, 25 Aug 2012 04:26:21 -0400 (EDT)
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- References: <20120824090532.3FD59684A@smc.vnet.net>
eqn = 16^(x*x + y) + 16^(x + y*y) == 1; If you guess from the symmetry that perhaps x == y sol = Solve[{eqn, x == y}, {x, y}, Reals][[1]] {x -> -(1/2), y -> -(1/2)} Verifying that assumption, eqn /. sol True >From this assumption the solution can be arrived at any number of ways. Reduce[{eqn, x == y}, {x, y}, Reals] // ToRules {x -> -(1/2), y -> -(1/2)} FindInstance[{eqn, x == y}, {x, y}, Reals][[1]] {x -> -(1/2), y -> -(1/2)} FindRoot[{eqn, x == y}, {{x, 1}, {y, 1}}] {x -> -0.5, y -> -0.5} Bob Hanlon On Fri, Aug 24, 2012 at 5:05 AM, <mainakju05 at gmail.com> wrote: > Find the value of x & y. We have only one equation: 16x.x+y + 16x+y.y = 1(16 to the power x.x + y + 16 to the power x+y.y = 1. > > I have found that X =-1/2 & y = -1/2 satisfying this equation. But I got it through trial method. It will be helpful, if anyone can solve this. >
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- Find the value of x & y
- From: mainakju05@gmail.com
- Find the value of x & y