A) 5, 11
B) 3, 5
C) 11, 17
D) 3, 7
Correct Answer: C
Solution :
\[|x-y|\le |x|-|y|\] Put \[x=\frac{3}{4},y=-\frac{1}{4}.\] Then, \[|x-y|=\left| \frac{3}{4}-\left( -\frac{1}{4} \right) \right|=\left| \frac{3}{4}+\frac{1}{4} \right|=1\] And \[\left| x \right|-\left| y \right|=\left| \frac{3}{4}-\left( -\frac{1}{4} \right) \right|=\left| \frac{3}{4}+\frac{1}{4} \right|=1\] Clearly, \[\left| x-y \right|\le \left| x \right|-\left| y \right|\] is a wrong statement
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