Question

find the value of (x+1/x)2​

Answer 1

Answer:

Case 1:

[math]x>0[/math]

By applying the [math]AM-GM[/math] inequality, we get:

[math]x+1/x>=2[/math]

With equality holding for the case, [math]x=1/x = 1[/math]

So, [math]x- 1/x = 0[/math], for [math]x>0[/math]

Case 2:

[math]x<0[/math]

If [math]x<0[/math], then so is [math]1/x[/math].

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

So, this case is void.

Hence, we get:

[math]x- 1/x = 0[/math], for all real x satisfying

Answer 2

Answer:

x+1 =1x /x=1, 1 ×2 =2

Step-by-step explanation:

it is your answer