Question

x+1/x=0 then show that. x-1/x​

Answer 1

Answer:

So basically we need to prove that f(x)>0∀x>0 .

f′(x)=1x+1−1(x+1)2=x(x+1)2>0∀x>0

Thus f(x) is a strongly increasing function.

As f(0)=0⇒f(x)>0∀x>0