mean inequality for 3 positive numbers - AM-HM-GM-RMS(QM)

[elhamasadi]

PROVE mean inequality for 3 positive numbers - AM-HM-GM-RMS(QM)
PROVE mean inequality for 4 positive numbers - AM-HM-GM-RMS(QM)

 

[stapel]

PROVE mean inequality for 3 positive numbers - AM-HM-GM-RMS(QM)
PROVE mean inequality for 4 positive numbers - AM-HM-GM-RMS(QM)

What are your thoughts? What have you tried? How far have you gotten? Where are you stuck?

Please be complete. Thank you!