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## Homework Statement

so this is the question i've trid my best (over 2 hours trynig this and failed) can someone please help me

show that :

l a l < 1 and l b l<1 => l a + b l < l 1 + ab l

## Homework Equations

just a little bit on info , you can only stay from the lal < 1 and lbl <1 side to get to the other one

## The Attempt at a Solution

here's what i tried so fay

l a l < 1 and l b l<1 => l a b l < 1

=> -1 < ab < 1

=> 0 < 1 + ab <2

=> l 1 + ab l <2

l a l < 1 and l b l<1 => -2 < a + b < 2

=> l a + b l < 2

yup im pretty much stuck here..pleasee help(i can't say l a + b l < l 1 + ab l because they are both<2..