已知x=根号3+根号2,y=根号3-根号2,求2x^2-xy-y^2

2024-10-28 07:16:52
推荐回答(2个)
回答(1):

根号x:表示为sqrt(x)

解:因为x=sqrt(3)+sqrt(2),y=sqrt(3)-sqrt(2)
所以2x^2-xy-y^2=(x-y)(2x+y)
=[(sqrt(3)+sqrt(2))-(sqrt(3)-sqrt(2))][2(sqrt(3)+sqrt(2))+(sqrt(3)-sqrt(2))]
=2sqrt(2)(3sqrt(3)+sqrt(2))
=6sqrt(6)+4

回答(2):

x=√3+√2,y=√3-√2
x+y=2√3
x-y=2√2
2x^2-xy-y^2=(2x+y)(x-y)=[(x+y) +x ](x-y)=(2√3+√3+√2)*2√2
=4+6√6