# finding A and B while only product and sum are given [duplicate]

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.

## marked as duplicate by Martin R, clathratus, Jyrki Lahtonen, Alexander Gruber♦Apr 29 at 1:31

• Substitute $A=629/B$ in the first equation. – Thomas Shelby Apr 28 at 12:31
• The question gives everything. Extract $A$ or $B$ from the first, plug it in the second and solve. – Claude Leibovici Apr 28 at 12:32
• From the first equation, $B=54-A$. Substitute this into the second equation and you have a quadratic. – saulspatz Apr 28 at 12:32

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