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    A + B = 54 

`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

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ Substitute $A=629/B $ in the first equation. $\endgroup$ – Thomas Shelby Apr 28 at 12:31
  • $\begingroup$ The question gives everything. Extract $A$ or $B$ from the first, plug it in the second and solve. $\endgroup$ – Claude Leibovici Apr 28 at 12:32
  • 1
    $\begingroup$ From the first equation, $B=54-A$. Substitute this into the second equation and you have a quadratic. $\endgroup$ – saulspatz Apr 28 at 12:32

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


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

As A+B = 54 and from above,

A= 50.911 and B = 3.089 (approx)


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