Problem simplifying an equation

[mr.t]

Homework Statement

What is the steps between the two equations?

Homework Equations

$$P = a^{2}P+b^{2}P^{2}/(P+1) \Rightarrow P^{2}-(a^{2}+b^{2}-1)P-b^{2} = 0$$

Thanks!

 

[tiny-tim]

What is the steps between the two equations?

$$P = a^{2}P+b^{2}P^{2}/(P+1) \Rightarrow P^{2}-(a^{2}+b^{2}-1)P-b^{2} = 0$$

Thanks!

Hi mr.t!

i] put the a²P on the left

ii] multiply both sides by (P + 1)

 

[mr.t]

Hello Tiny-tim!
Putting the $$a^{2}P$$ to the left and multiply both sides with (P+1) gives:

$$(P+1)(P-a^{2}P) = b^{2}P^{2} \Rightarrow$$
$$\Rightarrow P^{2}-a^{2}P^{2}+P-a^{2}P-b^{2}P^{2} = 0 \Rightarrow$$
$$\Rightarrow P^{2}(1-a^{2}-b^{2})+P(1-a^{2}) = 0$$

But I still can't come to the final solution? :S

 

[Defennder]

I don't think the two steps are equivalent. Let b=0, then a^2=1 if $$P \neq 0$$. Substituting these into the second equation, we have a^2 = 1 only if $$P = 0$$

 

[mr.t]

It could be an error in the solution then no fun try to learn stuff when you end up spending your time figuring out the imposible...

thanks for your time anyway!