已知x-y=6,xy=20,求(x+y)^2的值

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已知x-y=6,xy=20,求(x+y)^2的值
已知x-y=6,xy=20,求(x+y)^2的值

已知x-y=6,xy=20,求(x+y)^2的值
x-y=6,xy=20,
求(x+y)^2
=(x-y )^2 + 4xy
= 36 + 80
= 116
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(x+y)^2
=x²+2xy+y²
=x²-2xy+y²+4xy
=(x-y)²+4xy
=6²+4×20
=116

x-y=6
两边平方
x²-2xy+y²=36
两边加上4xy
x²+2xy+y²=36+4×20
所以(x+y)²=116

(x+y)^2
=x²+2xy+y²
=x²-2xy+y²+4xy
=(x-y)²+4xy
=6²-4×20
=36-80
=-44

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