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

Status
Not open for further replies.

#### OMEsystem (X+1/X)≥2

What's the name of this equation?

Thanks,

#### hamidr_karami

##### Banned 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

##### Full Member level 5 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

##### Junior Member level 2 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

Status
Not open for further replies.