Solve an Equation, Please Help:

[hrhgroup]

Please help me solving these problem:

 

[wave-maniac]

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

 

[hrhgroup]

Thanks very much.