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
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
The easy way? (Solution)
