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Are x,y,z real?

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For one, AM-GM is valid for +ve reals. Here a,b,c can be any real numbers.

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Method 1:

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Thank you jagdish for the appreciation.

 Discussion Forums -> This Post 10 points    (2    in 2 votes )   [?]

Its easy to see that (y+z) is even. Hence let (y+z) = 2t.

The given equation is then x+t=10 which has 9 solutions one for each value of t, .

It easy to see that for each t, we have to solve y+z = 2t, which will have 2t-1 solutions.

Hence the total number of solutions = 1+3+5+...+17 = 92 = 81.

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