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 Sir Francis Drake hardships
What is Sir Francis Drake hardships
What are two different ways to describe and label the layers of the Earth?
Can u paraphrase the quote ”let things take their course”
You have a cylinder with a diameter of 15 inches and a height of 12 inches. What is the volume of the largest sphere thg will fit inside it? If you can will you
When was World War I?
A passenger on a boat moving at 1.70 m/s on a still lake walks up a flight of stairs at a speed of 0.60 m/s , as shown in the figure . The stairs are angled at
What are two different ways to describe and label the layers of the Earth?
What is a direct combination reaction?
What is a direct combination reaction?