已知x-y=3,x^2-y^2=24,求x^2+y^2的值.

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已知x-y=3,x^2-y^2=24,求x^2+y^2的值.已知x-y=3,x^2-y^2=24,求x^2+y^2的值.已知x-y=3,x^2-y^2=24,求x^2+y^2的值.x^2-y^2=(x

已知x-y=3,x^2-y^2=24,求x^2+y^2的值.
已知x-y=3,x^2-y^2=24,求x^2+y^2的值.

已知x-y=3,x^2-y^2=24,求x^2+y^2的值.
x^2-y^2
=(x-y)(x+y)=24
又x-y=3
3(x+y)=24
x+y=8
则
x^2+y^2
=[(x+y)^2+(x-y)^2]/2
=(8^2+3^2)/2
=(64+9)/2
=73/2
=36.5

已知：x-y=3…………(1)
由：x^2-y^2=24，得：
(x+y)(x-y)=24
将(1)代入，有：
3(x+y)=24
x+y=8…………………(2)
(1)+(2)，有：2x=11
解得：x=11/2
代入(2)，有：11/2+y=8
解得：y=5/2
x^2+y^2
=(11/2)+(5/2)^2
=121/4+25/4
=146/4
=73/2

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