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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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution The hard way? (spoiler) | Comment 1 of 3
Well, there might be a more direct way to get C + 1/B, but I just solved the three simultaneous equations.

A = 1/BC.

Substituting to eliminate A in the other two equations gives

1/BC + 1/C = 5 and B + BC = 29

Solving both for B gives

B = 1/(5C - 1) and B = 29/(1+C)

Setting them equal and inverting gives

(5C - 1) = (1+C)/29

Then C = 5/24
Then B = 24
Then A = 1/5

So C + 1/B = 5/24 + 1/24 = 1/4

  Posted by Steve Herman on 2015-10-18 09:08:04
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