Question

cho a,b thỏa mãn |a|<1,|b|<1.cmr:|a+b|\(\le\)|1+ab|

Answer 1

Với |a|<1; |b| <1 thì ta có:
\(\left(a^2-1\right)\left(b^2-1\right)>0\)
\(\Leftrightarrow\left(ab\right)^2+1>a^2+b^2\) \(\Leftrightarrow\left(ab\right)^2+2ab+1>a^2+2ab+b^2\)
\(\Leftrightarrow\left(ab+1\right)^2>\left(a+b\right)^2\)
\(\Leftrightarrow\left|ab+1\right|>\left|a+b\right|\left(đpcm\right)\)

Answer 2

0 và -1