Jan 6, 2008 #1 hrhgroup Full Member level 3 Joined Jun 27, 2005 Messages 158 Helped 17 Reputation 34 Reaction score 7 Trophy points 1,298 Activity points 2,139 Please help me solving these problem:
Jan 6, 2008 #2 W wave-maniac Full Member level 3 Joined May 5, 2001 Messages 156 Helped 3 Reputation 6 Reaction score 0 Trophy points 1,296 Location USA Activity points 1,772 Assuming a, b, c and d are real, this might be the proof: 1) (a+d)^2+(b-c)^2>=0 => a^2+b^2+c^2+d^2+2(ad-bc)>=0 => 1+2(ad-bc)>=0 =>2(ad-bc)>=-1 2) (a-d)^2+(b+c)^2>=0 => a^2+b^2+c^2+d^2-2(ad-bc)>=0 => 1-2(ad-bc)>=0 =>2(ad-bc)<=1 1&2 => -1<=2(ad-bc)<=1 => 0<=2|ad-bc|<=1 where a^2=a*a
Assuming a, b, c and d are real, this might be the proof: 1) (a+d)^2+(b-c)^2>=0 => a^2+b^2+c^2+d^2+2(ad-bc)>=0 => 1+2(ad-bc)>=0 =>2(ad-bc)>=-1 2) (a-d)^2+(b+c)^2>=0 => a^2+b^2+c^2+d^2-2(ad-bc)>=0 => 1-2(ad-bc)>=0 =>2(ad-bc)<=1 1&2 => -1<=2(ad-bc)<=1 => 0<=2|ad-bc|<=1 where a^2=a*a
Jan 6, 2008 #3 hrhgroup Full Member level 3 Joined Jun 27, 2005 Messages 158 Helped 17 Reputation 34 Reaction score 7 Trophy points 1,298 Activity points 2,139 Thanks very much.