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fomenos
2 years ago
5

Find the equation of the plane z = mx + ny + b which contains the points (0,0,6), (1,0,-3) and (0,2,5).

Mathematics
1 answer:
leonid [27]2 years ago
8 0
The three points give you three equations, which you can solve by your favorite method.
.. 0m +0n +b = 6
.. 1m +0n +b = -3
.. 0m +2n +b = 5

(m, n, b) = (-9, -1/2, 6)
so the equation of the plane can be written as
.. z = -9x -1/2y +6

_____
In standard form, this would be
.. 18x +y +2z = 12

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Answer:

no real solution is the answer

If you have to list your extraneous solutions somewhere, that would be x=0.

Step-by-step explanation:

Cool thing here is the radical, the thing with the square root, is already isolate.

So we need to square both sides as a first step.  (Whenever you raise both sides to even power, you must definitely check your solutions as some might not actually be solutions to the original equation)

So upon squaring both sides I get:

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Now I will write (x^2-4)^2 as (x^2-4)(x^2-4) and foil it!  This gives me:

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0 isn't actually a solution though because when you plug it in you get 4=-4 which is not true.

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