已知x+y=2,xy=0.5,求x2+y2与(x-y)2的值

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已知x+y=2,xy=0.5,求x2+y2与(x-y)2的值
已知x+y=2,xy=0.5,求x2+y2与(x-y)2的值

已知x+y=2,xy=0.5,求x2+y2与(x-y)2的值
x²+y²
=(x²+2xy+y²)-2xy
=(x+y)²-2xy
=2²-2×0.5
=4-1
=3
(x-y)²
=x²-2xy+y²
=(x²+2xy+y²)-4xy
=(x+y)²-4xy
=2²-4×0.5
=4-2
=2
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x^2+y^2
=(x+y)^2-2xy
=4-2*0.5
=3
(x-y)^2
=x^2+y^2-2xy
=(x+y)^2-4xy
=4-4*0.5
=2

x2+y2=x²+2xy+y²-2xy=(x+y)²-2xy=4-1=3

(x-y)2=x²-2xy+y²=x²+2xy+y²-4xy=(x+y)²-4xy=4-2=2

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