Topic
Let x and y be two real numbers that differ from -1. Which of the following conclusions is correct?
A. \(x + y + xy \ne – 1\)
B. \(x + y + xy = – 1\)
C. \(x + y \ne – 2\)
D. \(xy \ne – 1\)
Solution method – See details
Check each clause. Type the answer by giving an example.
Detailed explanation
We have: \(x \ne – 1 \Rightarrow x + 1 \ne 0\).
Similarly \(y + 1 \ne 0\). Therefore: \((x + 1)(y + 1) \ne 0\) or \(x + y + xy \ne – 1\)
Choose A.
C is wrong, for example \(x = 0,y = – 2\) satisfies but \(x + y = – 2\)
D is false, for example \(x = \frac{1}{2},y = – 2\) satisfies but \(xy = – 1\)
