Finding A and B with the sum and product of them

Question

Question:

If $A + B = 54$ and $AB = 629,$ find $A$ and $B.$

I am not sure how to approach this problem since the question itself does not give much clue. Please help, thanks!

Answer 1

Hint: With $$B=54-A$$ we get $$A(54-A)=629$$

Answer 2

Using $(A-B)^2 = (A+B)^2 - 4AB$ $$(A-B)^2 = 54^2 - 4(629) = 2287$$ $$A-B = \sqrt{2287} = 47.822(approx)$$

As A+B = 54 and from above,

A= 50.911 and B = 3.089 (approx)