Question

已知x的平方-y的平方=1,x-y=2分之1,则xy=

Answer 1

x²-y²=1
即：(x-y)(x+y)=1
又x-y=1/2 ①
所以，x+y=2 ②
①+②得：2x=5/2，则：x=5/4
①-②得：-2y=-3/2，则：y=3/4
所以，xy=15/16

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Answer 2

(x-y)(x+y)=1,x-y=1/2
x+y=2
(x+y)²-（x-y)²=4xy=4-1/4=15/4
=>xy=15/16

Answer 3

x²-y²=1
即(x+y)(x-y)=1,而
x-y=1/2,所以
x+y=1/(x-y)=2
解得x=5/4,y=3/4
xy=15/16

Answer 4

x+y= 1/1/2=2
x= 5/4
y= 3/4
xy=15/16

Answer 5

x^2-y^2=(x-y)(x+y)=1
x-y=1/2则x+y=2
解得x=5/4
y=3/4
则xy=15/16

Answer 6

x^2-y^2=(x+y)(x-y)=1 则x+y=2
于是 x=5/4,y=3/4
则 xy=15/16