Quadratic Equation

[vanbeersj]

y=A+Bx^-2+Cx^-4

If i let x = r^-4 then I have y=A+Br^1/2 +Cr

I am suppose to solve for x but I can't seem to get x.

 

[galactus]

Let \(\displaystyle r=x^{-2}\), then we get:

\(\displaystyle y=Cr^{2}+Br+A\)

Now, use the quadratic formula to find r and then x.

 

[vanbeersj]

if I use the quatratic equation on y = Cr^2 + Br +A I get a solution with all variables r = {-B +/- (B^2-4CA)^1/2}/2A and if I substitute r for x^-2 i get even more confused.

 

[galactus]

You are gong to get variables as a solution because there are variables as coefficients. I see no way to get a definitive solutions(s) from what you have.

 

[Deleted member 4993]

if I use the quatratic equation on y = Cr^2 + Br +A I get a solution with all variables

r = {-B +/- (B^2-4CA)^1/2}/(2C)

and if I substitute r for x^-2 i get even more confused.

The denominator should be 2C

\(\displaystyle r \, = \, \frac{-B\pm\sqrt{B^2-4AC}}{2C}\)

\(\displaystyle x^{-2} \, = \, \frac{-B\pm\sqrt{B^2-4AC}}{2C}\)

\(\displaystyle x^{2} \, = \, \frac{2C}{-B\pm\sqrt {B^2-4AC}}\)

\(\displaystyle x \, = \, \sqrt{\frac{2C}{-B\pm\sqrt {B^2-4AC}}}\)