已知X=根号3 根号2分之根号3减根号2,Y=根号3减根号2分之根号3加根号2,求根号下3X²—5XY+3Y²的

2024-12-16 12:48:40
推荐回答(1个)
回答1:

x=(根号3-根号2)/(根号3+根号2)
=(根号3-根号2)^2/[(根号3)^2-(根号2)^2]
=(根号3-根号2)^2
=5-2*根号6

类似可得 y=5+2*根号6
xy=1, x^2+y^2=(5-2*根号6)^2+(5+2*根号6)^2=98
故3X²—5XY+3Y²=289
根号3X²—5XY+3Y²=17