I is a point in triangle ABC such that angle IBA > angle ICA , angle IBC > angle ICB , BI cut AC at B' , CI cut AB at C' . PRove the : BB' < CC'
please help me i'm very thanks
and the second problem
a,b,c>0 prove the equation have 1 root :
d^3 - d(ab+bc+ca) - 2abc =0 .
from the equation and x,y,z >0 . ax+by+cz=xyz . Prove the inequality
x+y+z >= 2/d . (\sqrt[(a+d)(b+d)(c+d)])
C)in assemble N ,every number is white or black so that white + black=black
prove : white + white = white