pr3tz81scut2
pr3tz81scut2 pr3tz81scut2
  • 03-10-2019
  • Mathematics
contestada

Prove the inequalities. c+ 1/c ≥2 for c>0

Respuesta :

LammettHash
LammettHash LammettHash
  • 03-10-2019

[tex]c+\dfrac1c=\dfrac{c^2+1}c=\dfrac{c^2-2c+1}c+2=\dfrac{(c-1)^2}c+2[/tex]

We have [tex](c-1)^2=0[/tex] when [tex]c=1[/tex], and for all other values of [tex]c[/tex] we have [tex](c-1)^2>0[/tex]. So

[tex]c+\dfrac1c=\dfrac{(c-1)^2}c+2\ge2[/tex]

Answer Link

Otras preguntas

what is 20/7 as a mixed number what is 9/4 as a mixed number what is 22/5 as a mixed number what is4/3 as a mixed number
Find all points having an x-coordinate of 4 whose distance from the point (-2,-1) is 10
4/3v^2x -5/6vx^3 what is this answer for algebra
What changes were made in Utah during World War 1?
is the earth getting heavier
What would be most useful to help make a simple compass a nonmetal bar,a round metal can,a small iron nail,or a Quartz needle
find the following sum and prove your claim: (1*2)+(2*3)+..+n(n+1).
who the famous artist in our time
is the earth getting heavier
is the earth getting heavier