Square roots

[Guest]

Can this equation be solved for B when B^2 is a very large number, and both A and B^2 are known, without having to take the square root of B^2 ?

B^2 = A^2 + (B+A)x(B-A) ? Where A is 7, and B^2 is 45,369

Thanks for the help.

[Guest]

The right side is

A^2+(B+A)(B-A)=A^2+B^2-A^2=B^2

[HallsofIvy]

B^2= A^2+ (B- A)(B+ A) is the same as B^2- A^2= (B- A)(B+ A) which is an identity- it is true for all A and B. Knowing that A= 7 doesn't help. If B^2= 45369 then B is the square root of 45369. The only way to determine B is to take the square root.

[Guest]

Mathematic lecture , Parabola function
https://youtu.be/V974YfDFSvo

[Guest]

Indeed the equation [tex]B^2= A^2+ (B+ A)(B- A)[/tex]
is exactly the same as [tex]B^2= A^2+ B^2- A^2[/tex] or
[tex]B^2= B^2[/tex] which is true for all values of A and B.

[Guest]

And, by the way, the square root of 45369 is B= 213. It's not that hard!