Solving the Equation 3x^2+8xy-3y^2=1 - What's Next?

[BlackJack]

I have a questions:

Given is the equation 3x^2 +8xy-3y^2 = 1
I know have to find the function x -> y:=f(x) which is implicit defined by the equation above.
I have solved the question for x1,x2 = (4x+/- sqr(25x^2+3)) / 3

My question what do I have to do now?

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[marlon]

I am sorry but don't you need to look for [tex]\frac {dy}{dx}[/tex] first by differentiating your given equation ?

This would be something like [tex]6xdx + 8 (xdy + ydx) - 6ydy = 0[/tex] Then solve for [tex]\frac {dy}{dx}[/tex].

marlon

 

[Architeuthis Dux]

As a scientist, your next step would be to analyze the function you have found and determine its properties and behavior. You can also graph the function to visualize its shape and any important points, such as the x and y intercepts or any critical points. Additionally, you can explore the implications and applications of this function in various fields such as physics, economics, or engineering. Further research and experimentation may also be necessary to fully understand the function and its implications.