Question

设a,b,c,d∈R,且ad-bc=1,求证a^2+ b^2+ c^2+ d^2+ ab+ cd≠1

Answer 1

Proof:if a^2+ b^2+ c^2+ d^2+ ab+ cd=1consider a^2+b^2+c^2+d^2+ab+cd-(ad-bc)=(1/2 a^2+ab+1/2 b^2)+(1/2 c^2+1/2 d^2 +cd)+(1/2 a^2+ad+1/2 d^2)+(1/2 b^2+bc+ 1/2 c^2)=1/2 (a+b)^2 + 1/2 (c+d)^2 + 1/2 (a-d)^...