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Sum Expression Value Determination (Posted on 2015-10-18) Difficulty: 3 of 5
Each of A, B and C is a positive real number satisfying this system of equations:
A*B*C = 1, A+1/C =5 and, B+1/A = 29

Find C+1/B

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution The easy way? (Solution) | Comment 2 of 3 |
Start with the product (A+1/C) * (B+1/A) * (C+1/B)

This can be expanded into A*B*C + A + B + C + 1/A + 1/B + 1/C + 1/(A*B*C)

Which can be arranged into A*B*C + (A+1/C) + (B+1/A) + (C+1/B) + 1/(A*B*C)

Substitute into the first and third forms of the expression the given values A*B*C=1, (A+1/C)=5, and (B+1/A)=29 to get:
5 * 29 * (C+1/B) = 1 + 5 + 29 + (C+1/B) + 1/1
145 * (C+1/B) = 36 + (C+1/B)
C+1/B = 1/4


  Posted by Brian Smith on 2015-10-18 13:12:59
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