I don't fully understand the logic of this example:
For, 4x^2-3x+5/(x-1)^2(x+2) we need: A/(x-1)^2+B/(x-1)+C/(x+2)
It is also correct to write Ax+B/(x-1)^2 + C/(x+2) but the fractions are not then reduced to the simplest form.
How do the 2nd fractions simplify to give the 1st set of...
Oh I have the solutions now! After getting a quartic in terms of y, I replaced y^2 with a which gave me a quadratic with 2 solutions, I then found the corresponding y values and then the x values. Thank you muchly for pointing out that my method was fundamentally flawed!
So what you're saying is that it's not possible to solve x^2(x^2-5)=-4 because there isn't a 0 on the right hand side? Instead we should substitute x^2 from the quartic equation and get a quadratic?
Thanks for the reply
Homework Statement x^2+y^2=5, 1/x^2+1/y^2=5/4
The Attempt at a Solution
I have rearranged the 1st equation: x^2=5-y^2
Then substitued this into the 2nd equation: 1/(5-y^2)+1/y^2=5/4
Found a common denominator: 5/(5x^2-x^4)=5/4
Multiply by the denominator...