MHB Finding Triples to Satisfy $\frac{5}{2}$

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The discussion focuses on finding all positive integer triples (a, b, c) that satisfy the equation a/b + c/a + b/(c+1) = 5/2. A participant points out a typo in the original post, where 'z' should have been 'c'. The author acknowledges the error and thanks the participant for the correction. The main goal remains to identify the valid triples that meet the specified equation. The conversation emphasizes clarity in mathematical expressions to avoid confusion.
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Find all triples $(a,\,b,\,c)$ of positive integers such that $\dfrac{a}{b}+\dfrac{c}{a}+\dfrac{b}{c+1}=\dfrac{5}{2}$.
 
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anemone said:
Find all triples $(a,\,b,\,c)$ of positive integers such that $\dfrac{a}{b}+\dfrac{c}{a}+\dfrac{b}{z+1}=\dfrac{5}{2}$.

what s z ?
 
It's a typo...$z$ is supposed to be a $c$.

I will fix my original post right now, and thanks for catching that...:D
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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