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

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OMEsystem

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(X+1/X)≥2

What's the name of this equation?

Thanks,
 

hamidr_karami

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Re: An inequality

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

kalyanram

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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

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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

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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
 

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