Solving Quadratic Equations with Parameters | Step-by-Step Guide

[razored]

Homework Statement

x=t^2 +t
y=t^2-t

Homework Equations

quadratic equation

The Attempt at a Solution

0=t^2-t-x
0=t^2+t+y
$$0=\frac{-1 +- \sqrt{1+4x}}{2} 0=\frac{1 +- \sqrt{1+4y}}{2}$$

Aftert i set the to quadratics equal to one another, I do not know what to do. Any help?

 

[Dick]

The results of the quadratic equations are t, not zero. But you are still doing it the hard way. Subtract the two original equations to get an expression for t in terms of x and y. Then substitute the resulting t back into one of the equations.

 

[tiny-tim]

x=t^2 +t
y=t^2-t

Hi razored!

Hint: go for the obvious … what is x + y?

 

[razored]

Subtracting y from x leaves me with $$0=x^2 -2xy+y^2-2y-2x$$ which is ugly. Is there anything I can do to find to y= ? No, right?

Thank you.

 

[Dick]

What's to do about it? You eliminated the parameter. Isn't that what they asked for? Trying to solve for y will just make it super-ugly.