mathuz wrote: if $a^2+b^2+c^2+d^2=1$ prove that \[ (1-a)(1-b)\ge cd. \] A. Khrabrov we know $\frac{c^{2}+d^{2}}{2}\geq cd$ so we must prove that : $a^{2}+b^{2}+1+2ab\geq 2a+2b\Leftrightarrow (a+b-1)^{2}\geq 0$

mathuz wrote: if $a^2+b^2+c^2+d^2=1$ prove that \[ (1-a)(1-b)\ge cd. \] See here: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=151&t=111267