SOLUTION: If 0 < a < b, show that a < sqrt{ab} < b.
Note: The number sqrt{ab} is called the geometric team of a and b.
Algebra ->
Inequalities
-> SOLUTION: If 0 < a < b, show that a < sqrt{ab} < b.
Note: The number sqrt{ab} is called the geometric team of a and b.
Log On
0 < a < b
Multiply through by a:
Nonnegative square roots are in the same order of inequality as their squares.
So we take nonnegative square roots:
0 < a < b
Multiply through by b:
Nonnegative square roots are in the same order of inequality as their squares.
So we take nonnegative square roots:
and
Therefore
Edwin
