Quadratic formula equation help?

Question

Is there anyway for me to use the quadratic formula for the following equation:

y^2-xy-x^2=0

I have tried many ways to solve this problem, but the answer keeps coming back as undefined. I even tried to graph this equation in 3-D and it came back saying that the equation was undefined. Can somebody help me figure out what to do here?

Answer 1

The quadratic formula will only help you solve for one of the variables.

For example... If you wanted to solve the equation for y, then in the quadratic formula, a = 1, b = -x and c = -x^2

You can't solve a single equation with two variables.  You need two equations in order to solve for two variables.

Answer 2

x1 = (-sqrt(5) abs(y)-y)/2

x2 = (sqrt(5) abs(y)-y)/2

Answer 3

There sure is!! You can solve for x in terms of y (or vice versa) using the quadratic formula. I'll show you how to do the former, i.e., find x in terms of y, after which one can find y in terms of x (if needed).

A. The "classic" form of the quadratic equation (QE) is

a*x^2 + b*x + c = 0

B. In your equation, a = - 1, b = - y and c = + y^2

C. Then, after simplifying the arithmetic and then some, the two

solutions are

x = [y + sqrt(y^2 + 4*y^2)] / ( - 2) = [- y/2]*[1 + sqrt(5)]

and also

x = [- y/2]*[1 - sqrt(5)]

D. From these results and/or by using the same process as above,

you can also find that

y = [x/2]*[1 + sqrt(5)] and y = [x/2]*[1 - sqrt(5)]

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I hope this helps.

Answer 4

Whenever you have two unknowns and only one equation, there are an infiinite number of solutions.  The solution is a line.