Question

if x =1+, then find {x+²​

Answer 1

Answer:

We may construct two cases, depending on whether x>0, or x<0 ( Obviously x≠0 )

Case 1:

x>0

By applying the AM−GM inequality, we get:

x+1/x>=2

With equality holding for the case, x=1/x=1

So, x−1/x=0 , for x>0

Case 2:

x<0

If x<0 , then so is 1/x .

But, if both are less than 0 , then their sum must also be less than 0 , and hence cannot be 2 .

So, this case is void.

Hence, we get:

x−1/x=0 , for all real x satisfying x+1/x=2