Yes I know i tried it out first and didn't knowif its alright to use the same method bec I couldn't remember how inequalities work at this point
Thats said it is shorter probably if I didn't make any mistake...I though I absolutely did
I think I got it?
If x>0 and y>0
Then |x+y |= x+ y and | xy+1|=xy +1
We have to prove that x+y < xy +1
X-1 < xy -y
X-1 < y(x-1) / x-1<0
1>y which is true tgeb x+y <xy+1
--if x and y are negative
|x+y |= -x-y and xy +1>0 then |xy+1 |=xy +1
Let us prove again thet -x-y <xy +1
-x-xy<1+y
-x(1+y)<...
Homework Statement
X and Y 2 real numbers / |x| <1 and |y|<1
Prove that |x+y|<|xy+1|
Homework Equations
The Attempt at a Solution
|x+y|<2
I couldn't prove that |xy+1| >2
And couldn't find a way to solve the problem
Please help