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#### eddybob123

##### Active member

- Aug 18, 2013

- 76

2. Let x, y, and z be positive real numbers such that

$$xyz=945$$

and

$$x(y+1)+y(z+1)+z(x+1)=385$$

What is the minimum possible value of \(\displaystyle z+\frac{y}{2}+\frac{x}{4}\)?

3. Let \(\displaystyle A\) be a 6x6 matrix such that \(\displaystyle A^k\) is the identity matrix for some positive integer \(\displaystyle k\). The smallest \(\displaystyle k\) is called the order of \(\displaystyle A\). What is the largest possible order of \(\displaystyle A\)?

4. What is the most number of non-parallel lines in 7 dimensional space such that the angle between any two of them is the same?

Enjoy!