Question

prove that : |x-y|<|x|+|y|​

Answer 1

Answer:

Let x be 10 and y be 4

|10-4|<|10+4|

| 6 | < | 14 |

so 14 is greater

so |x+y| is greater

Answer 2

Step-by-step explanation:

To Prove :

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

Proof:

We know that,

| x | = max {x, -x }

Therefore,

we get,

$±x ≤ |x |$

Now,

we have,

$x + y \leqslant |x| + y \leqslant |x| + |y| \\ \\ and \\ \\ - x - y \leqslant |x| - y \leqslant |x| + |y|$

From this,

we conclude that,

$= > |x + y| \leqslant |x| + |y|$

Now,

Put x = x and y = -y

we get,

$= > |x + ( - y)| \leqslant |x| + | - y|$

But,

we know that,

$| - y| = y$

Therefore,

we get,

$= > |x - y| \leqslant |x| + |y|$

Hence,

Proved