Question

Find the set the solves Formula1" title="x + \frac{2}{x} \geq 3" alt="x + \frac{2}{x} \geq 3" align="absmiddle" class="latex-formula">

Answer 1

Hello,
To exist x≠0

if x>0 then
x+2/x>=3==>x²+2>=3x
==>x²-3x+2>=0
==>(x-2)(x-1)>=0 positive out of the roots
==>  (x<=1 or x>=2) and x>0
==>(0<x<=1) or (x>=2)
else
x<0
x+2/x>=3==>x²+2<=3x
==>x²-3x+2<=0 negative betheen the roots
==>(1<=x<=2) and x<0 : no solution
end if