Question

Which of the following satisfies.

$|x+y|<|x|+|y|$

• A. x = 5, y = 2
• B. x = -5, y = 3
• C. x = -2, y = -5
• D. x = 5, y = -2

Answer 1

The correct option is D

x = 5, y = -2

For x = 5 & y = -2

$|x+y|<|x|+|y|$

$\Rightarrow |5+(-2)|<|5|+|-2|$

$\Rightarrow |5-2|<|5|+|-2|$

$\Rightarrow |3|<|5|+|2|$

$\Rightarrow 3<5+2$

$\Rightarrow 3<7$ which is true.

$\therefore$ x = 5 & y = -2