If I have an equation like this

[2f+(p+q) ]*[2f-(p+q) ]=4pq


Are any of the three methods below any better than the other?

Are any of them incorrect?
Is there a 'correct' way that should always be used?

Many thanks


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Method 1.


[2f+(p+q) ]*[2f-(p+q) ]=4pq

let\ \ \ 4pq=rs


2f+(p+q)=r


2f-(p+q)=s


4f=r+s\ \ \ \ \ \ \ \ \ \ f=\dfrac{r+s}{4}


2(p+q)=r-s\ \ \ \ \ \ \ \ p+q=\dfrac{r-s}{2}


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Method 2.


[2f+(p+q) ]*[2f-(p+q) ]=4pq

let\ \ \ 4pq=4rs

2f+(p+q)=2r

2f-(p+q)=2s

4f=2r+2s\ \ \ \ \ \ \ \ \ \ \ f=\dfrac{r+s}{2}

2(p+q)=2r-2s\ \ \ \ \ \ \ \ p+q=r-s

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Method 3.


[2f+(p+q) ]*[2f-(p+q) ]=4pq

let\ \ \ 4pq=4rs

2f+(p+q)=4r

2f-(p+q)=s

4f=4r+s\ \ \ \ \ \ \ \ \ \ \ \ \ f=\dfrac{4r+s}{4}

2(p+q)=4r-s\ \ \ \ \ \ \ \ p+q=\dfrac{4r-s}{2}