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Answer:
Given the equation:
\(\frac{XYZ][8] = \frac{ZY][8]\)
We are asked to find the three-digit number XYZ where X, Y, and Z are different non-zero digits.
To solve this, we can express the fractions as decimal numbers:
\(\frac{XYZ][8] = \frac{ZY][8] \Rightarrow 100X + 10Y + Z = 10Z + Y
From the equation above, we can simplify it to:
\(100X + 10Y + Z = 10Z + Y\)
Rearranging the terms gives us: \(100X +9Y = 9Z\)
Given that X, Y, and Z are different non-zero digits, we can start by trying different combinations to find a suitable solution.
Let's explore a possible solution:
If X = 1, Y = 2, and Z = 3:
Plugging these values into the equation gives us:
\(100(1) +9(2) = 9(3)\)
\(100 + 18 = 27)
\(118 \neq 27)
Therefore, the solution X = 1, Y = 2, and Z = 3 is not valid.
Continue exploring different combinations until you find the correct values for X, Y, and Z that satisfy the equation.