square of (|x|-|y|)=x^2+y^2-2|x|*|y|
square of |x-y|=(x-y)^2=x^2+y^2-2xy
square of |x|+|y|=x^2+y^2+2|x|*|y|
now for all x x|≤x|
gves 2|x|*|y| greater than or equal to 2xy
so we can see that square of (|x|-|y|)<= square of |x-y|
take square root on both sides
since |x-y| is always positive
|x|-|y|≤|x-y|
looking at square of |x|+|y| we can clearly see that it is greater than |x|+|y| since it is always x^2+y^2+ a positive number
so |x|-|y|≤|x-y|≤|x|+|y| is true in math
because it works. input numbers and see yourself.
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square of (|x|-|y|)=x^2+y^2-2|x|*|y|
square of |x-y|=(x-y)^2=x^2+y^2-2xy
square of |x|+|y|=x^2+y^2+2|x|*|y|
now for all x x|≤x|
gves 2|x|*|y| greater than or equal to 2xy
so we can see that square of (|x|-|y|)<= square of |x-y|
take square root on both sides
since |x-y| is always positive
|x|-|y|≤|x-y|
looking at square of |x|+|y| we can clearly see that it is greater than |x|+|y| since it is always x^2+y^2+ a positive number
so |x|-|y|≤|x-y|≤|x|+|y| is true in math
because it works. input numbers and see yourself.