SOLUTION: Can you please help me with those problems??? 1. Suppose that |a - b| + |b - c| + |c - d| + ... + |x - y| + |y - z| + |z - a| = 20: What is the maximum possible value of |a

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Question 486605: Can you please help me with those problems???
1. Suppose that
|a - b| + |b - c| + |c - d| + ... + |x - y| + |y - z| + |z - a| = 20:
What is the maximum possible value of |a - b|? What is the maximum possible value of |a - n|?
2. For what constants k does the equation
k2^x + 2^-x = 3 have only one real solution x?
3. How many positive integers n satisfy square root of n equal to 5.
Thank you very much for your help!!!!
Answer by chessace(471) (Show Source):
You can put this solution on YOUR website!
1.
This is the formula for the total distance between a set of points (round trip).
So the max for any term and for any unlisted "distance" will be half the round trip total, with a bunch of points either identical or in the "same direction".
Answer = 10 to both parts.
2.
Only k=0. If you don't get rid of one of those x's, there will be an even number (0 or 2) of real solutions.
3.
Only one, 25.

SOLUTION: Can you please help me with those problems??? 1. Suppose that |a - b| + |b - c| + |c - d| + ... + |x - y| + |y - z| + |z - a| = 20: What is the maximum possible value of |a - b