设a,b,c,d是实数,且ad-bc=1,a²+b²+c²+d²-ab+cd=1,求abcd的值
问题描述:
设a,b,c,d是实数,且ad-bc=1,a²+b²+c²+d²-ab+cd=1,求abcd的值
kuai
答
2a²+2b²+2c²+2d²-2ab+2cd=22a²+2b²+2c²+2d²-2ab+2cd=2(ad-bc)2a²+2b²+2c²+2d²-2ab+2cd-2ad+2bc=0(a²-2ab+b²)+(c²+2cd+d²)+...=...