Question

已知x=根号3+根号2,y=根号3-根号2,求2x^2-xy-2y^2

Answer 1

x=根号3+根号2,

y=根号3-根号2

xy=1, x+y=2√3,x-y=2√2

2x^2-xy-2y^2

=2（x+y)(x-y)-xy

=2*2√3*2√2-1

=8√6-1