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?

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

Ahoy,

 

OK, thanks 4/5 I can't believe I didn't see that.

 

Arrrhhhhhhh

Edited May 18, 201114 yr by CaptainBlood