Question

已知x=根号3+根号2分之根号3-根号2, y=根号3-根号2分之根号3+根号2

求x²+y²的值

Answer 1

x=根号3+根号2分之根号3-根号2=(√3-√2)/(√3+√2)=(√3-√2)^2/(√3+√2)(√3-√2)=5-2√6
y=根号3-根号2分之根号3+根号2=(√3+√2)/(√3-√2)=(√3+√2)^2/(√3+√2)(√3-√2)=5+2√6
x²+y²=(5-2√6)^2+(5+2√6)^2=98

Answer 2

分母有理化
x=(√3+√2)²=5+2√6
y=(√3-√2)²=5-2√6
所以x+y=10
xy=25-24=1
所以x²+y²=(x+y)²-2xy=100-2=98

Answer 3

x=根号3+根号2分之根号3-根号2
=(√3-√2)/(√3+√2)
=(√3-√2)^2/(√3+√2)(√3-√2)
=3-2√6+2/3-2
=5-2√6
y=根号3-根号2分之根号3+根号2
=(√3+√2)/(√3-√2)
=(√3+√2)^2/(√3+√2)(√3-√2)
=3+2√6+2/3-2
=5+2√6

x²+y²
=(5-2√6)^2+(5+2√6)^2
=25-20√6+24+25+20√6+24
=98