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If (x,y) satisfies the simultaneous equations

3xy - 4x^2 - 36y + 48x = 0

x^2 - 2y^2 = 16 
where x and y may be complex numbers, determine all possible values of y^2.

Guest Feb 27, 2018
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 #1
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helpppppppppppp

Guest Feb 28, 2018
 #2
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3xy - 4x^2 - 36y + 48x = 0   (1)

x^2 - 2y^2 = 16   (2)

 

Look at the graph here :

 

https://www.desmos.com/calculator/kfu7s3izs1

 

Note that, oddly, the first graph is a straight line ......this is known as a "degenerate conic" which never intersects the second function (a hyperbola)....so....no solutions

 

 

 

cool cool cool

CPhill  Feb 28, 2018

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