Recent content by liluiass

  1. liluiass

    Prove: |x+y|<|xy+1| for |x|,|y|<1

    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
  2. liluiass

    Prove: |x+y|<|xy+1| for |x|,|y|<1

    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)<...
  3. liluiass

    Prove: |x+y|<|xy+1| for |x|,|y|<1

    Homework Statement X and Y 2 real numbers / |x| <1 and |y|<1 Prove that |x+y|<|xy+1|Homework EquationsThe 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