What are values of P such that P/P +1/P <1

Question

what are values of P such that P+1⁄P < 1

Answer 1

If P + 1/P < 1, then (P² + 1) / P < 1

 

So, (P² + 1) / P - 1 < 0

 

(P²-P+1) / P < 0

 

P² - P + 1 = P² - P + 1/4 + 3/4 (by completing the square)

 

                = (P - 1/2)² + 3/4 > 0 for all real numbers, P

 

So, since (P²-P+1) / P < 0 and the numerator is always positive, the denominator, P, must be negative.

 

Therefore, P < 0.  

 

                 

Answer 2

I think it's the set of negative number...

 

Can't use 0 because it's undefined.

 

If P = -1, then you get 0 < 1, which is true.

 

If P = -2, then you get 1/2 < 1, which is true.

 

And so on.