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July 29th, 2010, 06:30 PM   #1
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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
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July 29th, 2010, 07:23 PM   #2
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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]
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July 30th, 2010, 01:00 PM   #3
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Re: Three Variables 3 Equations with Exponents

Quote:
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.
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