Question

已知x+y=2√5-√3,x-y=2√3-√5

(1)求x²-y²的值
(2)求x²+y²-xy的值

Answer 1

解：因搜差清为x+y=2倍根号5-根号3
x-y=2倍根号3-根号5
所以x=根号5+根号3/2
y=3(根号5-根号3)/2
xy=3/庆和2
(1)x^2-y^2
=(x+y)(x-y)
=5倍根世前号15-16
（2）x^2+y^2-xy
=(x+y)^2-3xy
=23-4倍根号15-9/2
=37/2-4倍根号15

Answer 2

Answer 3

(1)x²-y²=(x+y)(x-y)=(2√5-√3)(2√3-√5)=4√弯唯15+√15-6-10=5√15-16
(2)x²+y²-xy=1/桐兄4(x+y)²+3/4(x-y)²=1/4(23-4√埋轮培15)+3/4(17-4√15)=37/2-4√15

Answer 4

x=（√5+√3）/2
y=3（√5-√3）/2
x²-y²=（x+y）码档扒（x-y）=（2√5-√3）（2√蠢碧3-√5）迟昌=5√15-16