Question

已知(x-y)的2次方=625/36,x+y=7/6,求xy的值

Answer 1

已知(x-y)²=625/36,x+y=7/6
那么(x+y)²=49/36
因为(x+y)²=x²+y²+2xy
(x-y)²=x²+y²-2xy
所以(x+y)²-(x-y)²=4xy
所以4xy=49/36-625/36=-576/36
所以xy=-144/36=-4

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Answer 2

(x-y)的2次方=625/36
x²-2xy+y²=625/36 (3)
x+y=7/6
x²+2xy+y²=49/36 (4)
（4)-(3)得
4xy=-576/36
∴xy=-4

Answer 3

(x-y)的2次方=625/36
x^2+y^2-2xy=625/36
,x+y=7/6
(x+y)^2=49/36
x^2+y^2+2xy=49/36
4xy=-576/36
xy=-4

Answer 4

(x-y)的2次方=x²-2xy+y²=625/36

x²+y²=625/36+2xy

x+y=7/6

(x+y)²=49/36
x²+2xy+y²=49/36
625/36+2xy+2xy=49/36

4xy=-576/36
xy=-144/36
xy=-4