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1. Find constants A and B such that \(\frac{x + 7}{x^2 - x - 2} = \frac{A}{x - 2} + \frac{B}{x + 1}\) for all x such that x ≠ -1 and x ≠ 2. Give your answer as the ordered pair (B,C).

 

 

2. Suppose that \(|a - b| + |b - c| + |c - d| + \dots + |m-n| + |n-o| + \cdots+ |x - y| + |y - z| + |z - a| = 20.\) What is the maximum possible value of \(|a - n|\)?

 Jun 19, 2020
 #1
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1. (A,B) = (4,-7).

 

2. By the triangle inequaity, any two variables differ by at most 20, so the maximum value of |a - n| is 20.

 Jun 19, 2020
 #2
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Sorry that isn't correct.

Guest Jun 19, 2020
 #3
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The first one is quite simple.

Treat it like any other algebraic fraction ONLY always keep the two sides seperate.

Get a common denominator for the RHS then equate cooefficients.

 Jun 20, 2020

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