Question

设x等于根号3减2分之—,y等于根号3加2分之—,求代数式x加y分之x的平方加xy加y的平方

Answer 1

x+y=根号3减2分之—+根号3加2分之—=2根号3
xy=根号3减2分之—×根号3加2分之—=3-1/4=11/4
x²+xy+y²=x²+2xy+y²-xy=（x+y）²-xy=12-11/4=37/4
所以原式=（37/4）/2根号3=37根号3/24

Answer 2

x^2/(x+y)+y^2/(x+y)
=(x^2+y^2)/(x+y)
=[(x+y)^2-2xy]/(x+y)
=(x+y)-2xy/(x+y)
=(√3-1/2+√3+1/2)-2(√3-1/2)(√3+1/2)/(√3-1/2+√3+1/2)
=2√3-2*(3-1/4)/2√3
=2√3-√3+√3/12
=13√3/12

Answer 3

(266根号3+109）/88