Let . If , prove that .
Tag: General
An identity
If , prove that
Trigonometry with golden ratio
Let denote the golden ratio. Prove that
Solution
Since we deduce that . Furthermore,
Also, taking into consideration that we deduce that:
In the last step we made use of the identity .
A complex inequality
Let such that and . Prove that .
Solution
We have successively:
Floor of square root
Let be a positive real number. Prove that
Solution
We have successively: