若x=(2+√3)/(2-√3),y=(2-√3)/(2+√3),求2x²;-3xy+2y²;
问题描述：
若x=(2+√3)/(2-√3),y=(2-√3)/(2+√3),求2x²;-3xy+2y²;
答
2x²=2[(2+√3)/(2-√3)]²=2(4+4√3+3)/ 4-4√3+4=2(7+4√3)/7-4√3
=2(7+4√3)²/(7+4√3)(7-4√3)
=2（49+56√3+48）
=194+112√3
-3xy+2y²=-3[(2+√3)/(2-√3)]x[(2-√3)/(2+√3)]+2[(2-√3)/(2+√3)]²
=-3+2(7-4√3)/7-4√3
=-3+2(7-4√3)²/(7+4√3)(7-4√3)
=-3+194-112√3
=191-112√3
答
xy=1.
x+y=(2+√3)/(2-√3)+(2-√3)/(2+√3)=(2+√3)^2+(2-√3)^2=14
2x²-3xy+2y²
=2(x+y)²-7xy
=385