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 3,200,000,000,000 in scientific notation
Analyze how scientific thhought changes as new information is collected
Write 0.632 in 2 forms
Two trains leave the station at the same time, one heading East and the other heading West. The westbound train is going 60mph. The eastbound train is going 80m
The 10th and the 20th term of an arithmetic sequence are 10 and 40, respectively. Find its 100th term.
why is the use of the inquiry process a practical way to approach science HELP
What is the GCF of 32 and 48
dose anyone know how to solve any of these? 1. W is the midpoint of UV. if UW= x+23, and WV= 2x+8, what is x? 2. W is the midpoint of UV. if UW= x+23, and WV= 2
8 times 51 show your work
What effect did the Revenue Act of 1926 have on Americans?