10> Y > Z, n is a natural number, 1 / (X-Y) + 2 / (Y-Z) > = n / (x-z), the maximum value of n is

Let X-Y = a, Y-Z = B, then x-z = a + B
1/a+2/b-n/(a+b)>=0
Multiply AB (a + b)
b(a+b)+2a(a+b)-nab>=0
b²+2a²+3ab-nab>=0
2(a-b/√2)²+2√2ab+3ab-nab>=0
So as long as 2 √ 2Ab + 3AB nab > = 0
n

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