若(x-y)²=4,(x+y)²=16,则x²+y²等于

若(x-y)²=4,(x+y)²=16,则x²+y²等于
若(x-y)²=4,(x+y)²=16,则x²+y²等于

若(x-y)²=4,(x+y)²=16,则x²+y²等于
x²+y²
=[(x+y)²+(x-y)²]／2
=(16+4)/2
=10

(x+y)²-(x-y)²=4xy=16-4=12
xy=3

(x+y)²=x²+y²+2xy=16
x²+y²=16-2xy=16-2*3=10

由已知可得
x^2-2xy+y^2=4
x^2+2xy+y^2=16
两式相加得出
2x^2+2y^2=20
x^2+y^2=10

(x-y)²=4 (1)
(x+y)²=16 (2)
由（1）得
x²-2xy+y²=4 (3)
由（2）得
x²+2xy+y²=16 (4)
(3)+(4)得
2（x²+y²）=20
解得x²+y²=10