Xy=42(x

It seems like there might be some confusion in your question with the notation used. Let's clarify the expression you've written.

You appear to have two cases, depending on the relationship between \(x\) and \(y\):

1. \(xy = 42\) when \(x < y\)
2. \(xy = 40\) when \(x > y\)

To solve for \(x\) and \(y\), we can analyze each case separately.

### Case 1: \(x < y\) and \(xy = 42\)

From \(xy = 42\), we can express \(y\) in terms of \(x\):
\[
y = \frac{42}{x}
\]
Since \(x < y\), we substitute for \(y\):
\[
x < \frac{42}{x}
\]
Multiplying both sides by \(x\) (assuming \(x > 0\)):
\[
x^2 < 42
\]
Thus,
\[
x < \sqrt{42} \approx 6.48
\]

### Case 2: \(x > y\) and \(xy = 40\)

From \(xy = 40\), we can again express \(y\) in terms of \(x\):
\[
y = \frac{40}{x}
\]
Since \(x > y\), we substitute for \(y\):
\[
x > \frac{40}{x}
\]
Multiplying both sides by \(x\) (assuming \(x > 0\)):
\[
x^2 > 40
\]
Thus,
\[
x > \sqrt{40} \approx 6.32
\]

### Conclusion
Now we have two intervals for \(x\):

1. From the first case: \(0 < x < \sqrt{42}\) (approximately 6.48)
2. From the second case: \(x > \sqrt{40}\) (approximately 6.32)

The valid solution for \(x\) must satisfy both conditions, meaning:
\[
\sqrt{40} < x < \sqrt{42}
\]

This leads to an interval for \(x\):
\[
6.32 < x < 6.48
\]

You can then substitute values within this range back to find corresponding values of \(y\) using \(y = \frac{42}{x}\) or \(y = \frac{40}{x}\) depending on whether \(xy\). Would you like to proceed with specific calculations or have more questions on this topic?