How would I go about finding x and y? |x| + |y| = |x + y|

Question

anonymous · Answer

i think you make your own example 
like 5+3=8

welshfella · Answer

there are infinite solutions

for example

|1! + |2|  = |1 + 2|

and many ,many more

anonymous · Answer

I think the thing that I am more confused with is what would x and y have to be (such as negative or positive) that would be right, sorry I didn't explain the question correctly
I mean for |x| + |y| < |x+y| xD

zzr0ck3r · Answer

This is always true, just to let you know...it may help

$$|a+b|\le |a|+|b|$$

anonymous · Answer

What you have is less than or equal to. I am thinking more of just less than, and switched around

zzr0ck3r · Answer

you will never find $|a|+|b|<|a+b|$

anonymous · Answer

Interesting, How would you interpret the word problem: "Write the statement where the sum of the absolute values of two numbers is less than the absolute value of the sum of the two numbers."

welshfella · Answer

you interpreted it correctly

anonymous · Answer

So that would interpret to |x|+|y|<|x+y|? and if so, there must be some value for x and y that would make the equation true, correct?

zzr0ck3r · Answer

There is not.


$$a^2+b^2+2|a||b|\ge a^2+b^2+2ab$$

Now $|a|^2=a^2$ for any number $a$. So from above

$$|a|^2+|b|^2\ge |a+b|^2\implies |a|+|b|\ge |a+b|$$