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 July 29th, 2010, 06:30 PM #1 Newbie   Joined: Jul 2010 Posts: 4 Thanks: 0 Three Variables 3 Equations with Exponents Good day everyone! I recently come across a interesting problem which I can not seam to solve. The equations are as; 4.5=sqrt[{x_o - x_a}^2 + {y_o - y_a}^2 +{z_o - z_a}^2] 4.5=sqrt[{x_o - x_b}^2 + {y_o - y_b}^2 +{z_o - z_b}^2] 4.5=sqrt[{x_o - x_c}^2 + {y_o - y_c}^2 +{z_o - z_c}^2] The bolded variables represent unknown values. From prior experience I would assume it is possible to solve this the but exponents are throwing me off. If anyone could help steer me in the right direction that be great. I very much appreciate the help. Taylor S. Amarel Learning is living July 29th, 2010, 07:23 PM #2 Senior Member   Joined: Aug 2008 From: Blacksburg VA USA Posts: 354 Thanks: 7 Math Focus: primes of course Re: Three Variables 3 Equations with Exponents assuming eq'ns are distinct/not duplicitous thus (3) different solution sets well, start from the more standard form x1^2+y1^2+z1^2=4.5^2 x2^2+y2^2+z2^2=4.5^2 x3^2+y3^2+z3^2=4.5^2 Can you find a solution to the above? If you can, then can you xchange for each axis variable ones with a common offset? A simple example is say a solution x vector was (3,4,5). This becomes (10-7,10-6,10-5) where 10 is an arbitrary common x offset (your ). [Of course with the squaring the order for the offsets and variable vector points is mute to an xtent] July 30th, 2010, 01:00 PM   #3
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Re: Three Variables 3 Equations with Exponents

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 Originally Posted by tsa256 Good day everyone! I recently come across a interesting problem which I can not seam to solve. The equations are as; 4.5=sqrt[{x_o - x_a}^2 + {y_o - y_a}^2 +{z_o - z_a}^2] 4.5=sqrt[{x_o - x_b}^2 + {y_o - y_b}^2 +{z_o - z_b}^2] 4.5=sqrt[{x_o - x_c}^2 + {y_o - y_c}^2 +{z_o - z_c}^2] The bolded variables represent unknown values. From prior experience I would assume it is possible to solve this the but exponents are throwing me off. If anyone could help steer me in the right direction that be great. I very much appreciate the help. Taylor S. Amarel Learning is living
If you look at it geometrically, you have 3 spheres with different centers, but having the same radius. It looks like the answer is simply the points of intersection. Tags equations, exponents, variables Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post WWRtelescoping Complex Analysis 4 February 8th, 2014 07:56 PM Dreamyvarela Applied Math 1 January 8th, 2014 02:15 PM oshmunnies Algebra 12 August 13th, 2013 12:26 PM Russell368 Elementary Math 35 July 10th, 2011 08:32 PM morning_mood Algebra 6 December 21st, 2007 12:02 AM

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