已知x=1/2(√7+√5),y=1/2(√7-√5),求下列各式的值1.x^2-xy+y^22.x/y+y/x

Question

已知x=1/2(√7+√5) ,y=1/2(√7-√5),求下列各式的值
1.x^2-xy+y^2
2.x/y+y/x

Answer 1

1.x^2-xy+y^2
=(x-y)^2+xy
=[1/2(√7+√5) -1/2(√7-√5)]^2+1/2(√7+√5)×1/2(√7-√5)
=5+1/4×2
=5+1/2
=5.5
2.x/y+y/x
=(x^2+y^2)/xy
=[(x-y)^2+2xy]/xy
=(x-y)^2/xy+2
=[1/2(√7+√5)+1/2(√7-√5)]^2/[1/2(√7+√5) ×1/2(√7-√5)]+2
=5/(1/4×2）+2
=10+2
=12