Answer :

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.