CaptainBlood Posted May 18, 2011 Share Posted May 18, 2011 If the product of two numbers if 5, and the sum of these same two numbers is 4, what's the sum of the reciprocals of these two numbers? I tried: let's say we have two numbers a and b, then a*b = 5 a = 5/b since their product is 4, we get b + 5/b = 4 or b^2 -4b + 5 = 0 but this has no real solutions just imaginary because this function is > 0 for all b I can't factor it and the quadratic formula doesn't work since 4^2 < 4*1*5 also the derivative is 2b -4 = 0 so b = 2 is the minimum since second derivative is positive but that doesn't help either. What do I do? Link to comment Share on other sites More sharing options...
imatfaal Posted May 18, 2011 Share Posted May 18, 2011 Ahoy Capt You are complicating too much. To start with, try working out exactly what is being requested [math] the\ sum\ of\ the\ reciprocals = \frac{1}{a} + \frac{1}{b} [/math] Perhaps try rearranging/simplifying the RHS - once you do this the answer will jump out and hit you Link to comment Share on other sites More sharing options...
CaptainBlood Posted May 18, 2011 Author Share Posted May 18, 2011 (edited) Ahoy, OK, thanks 4/5 I can't believe I didn't see that. Arrrhhhhhhh Edited May 18, 2011 by CaptainBlood Link to comment Share on other sites More sharing options...
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