Question

已知x=根号3+根号2,y=根号3-根号2,求x的3次方+y+（xy）的3次方的值等于多少?

Answer 1

x=√3+√2

y=√3-√2

xy=(√3+√2)(√3-√2)=3-2=1

x^3+y+(xy)^3

=x^3+y+1

=(x+1)(x²-x+1)+y

=(√3+√2+1)(3+2+2√6-√3-√2+1)+√3-√2

=(√3+√2+1)(6+2√6-√3-√2)+√3-√2

=6√3+6√2+6+6√2+4√3+2√6-3-√6-√3-√6-2-√2+√3-√2

=10√3+10√2-1