Question

若x>y>0 （x-y）的平方除以xy 等于2 x方减y方除以xy 等于多少?

Answer 1

∵（x-y）²/(xy)= 2
∴(x-y)²=2xy (1)
x²+y²-2xy=2xy
∴x²+y²+2xy=6xy
(x+y)²=6xy (2)
(1)(2)两式两边相乘
(x-y)²(x+y)²=12x²y²
两边开平方:
∵x>y>0
∴(x-y)(x+y)=2√3*xy
即(x²-y²)/(xy)=2√3