Difficult simplification problem

I am trying to simplify this to express **a** as a function of **t,r,p**. It is killing me. Any help would be most appreciated.

a^2=[(at)^2 + r^2]/p

Edit: This problem is trivial, but I am also looking for a solution given the additional constraint,

t=ab,

Re: Difficult simplification problem

We are given to solve for :

The first step is to multiply through by :

Now, subtract through by :

Factor the left side:

Can you proceed from here?

Re: Difficult simplification problem

Okay, but (at)^2 does not equal a^2t^2, it equals a^2 +2at + t^2

I am stuck trying to get rid of the 2at term.

Re: Difficult simplification problem

however , but this is not what you posted.

Which do you mean?

Re: Difficult simplification problem

Sorry, I was writing and reading (at)^2 and thinking (a+t)^2. The former is the correct expression. Thank you for our help.

Re: Difficult simplification problem

Okay, what if we introduce a further identity,

t=ba

giving

A^2p - B^2A^4 = r^2

Is this soluble ?

Re: Difficult simplification problem

Re: Difficult simplification problem

I am confused, because your solution gives a=zero when b=0, but if we simply let b=0 and solve from the initial equation, we get a simple solution that is only zero when r=0, i.e.

a=SQRT(r^2/p)

Edit: I see that the quadratic formula does not apply when b=0.