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18 Apr 2020
Use the properties of inequalities to prove the following inequalities.
Rule 6 for Inequalities: If a, b, c, and d are any real numbers such that 
and 
then 
. [Hint: Use Rule 1 to show that and then 
.
Use the properties of inequalities to prove the following inequalities.
Rule 6 for Inequalities: If a, b, c, and d are any real numbers such that and then . [Hint: Use Rule 1 to show that and then .
Hubert KochLv2
26 May 2020
are positive number such that 
, and their geometric mean is
. The arithmetic-geometric mean inequality states that the geometric mean is always less than or equal to the arithmetic mean. In this problem we prove this in the case of two numbers x and y. If x and y are nonnegative and
, then 
[Hint: First use Rule 3 of Inequalities to show that 
]
│ is the distance between a and b on the number line. For any number x, what do 
and │
│ represent? Use this interpretation to solve the inequality │
│
│
│
│