What's the name of (X+1/X)≥2 equation?

[OMEsystem]

(X+1/X)≥2

What's the name of this equation?

Thanks,

 

[hamidr_karami]

Re: An inequality

hi
i don't know.
but i prove it.
hamid karami

 

[kalyanram]

Re: An inequality

I don't know if this inequality has a name. But in theory this is taught after the AM ≥ GM, then followed by saying that sum of a positive number and its reciprocal is always greater than or equal to 2.

~Kalyan.

 

[neils_arm_strong]

An inequality

I dont think there is any name for this equation.But the proof is very simple.Just differentiate the LHS of the equation and equate it to zero.This gives x=1 for extreme value(minimum in this case).Then substitiuting x=2 yields x+1/x=2.i.e minimum value of the expression is 2.

 

[whynot910]

Re: An inequality

in that inequality, the x must be larger than 0. and u can prove it just use the basic inequality a^2+b^2≥2ab