已知（x+y)²=18,（x-y)²=6,求：①x²+y²的值；②xy的值.

已知（x+y)²=18,（x-y)²=6,求：①x²+y²的值；②xy的值.
已知（x+y)²=18,（x-y)²=6,求：①x²+y²的值；②xy的值.

已知（x+y)²=18,（x-y)²=6,求：①x²+y²的值；②xy的值.
x²+y²
=[(x+y)²+(x-y)²]/2
=(18+6)/2
=24/2
=12
=12
xy=[(x+y)²-(x-y)²]/4
=(18-6)/4
=12/4
=3

(1)（x+y)²+（x-y)²=24
x²+2xy+y²+x²-2xy+y²=24
2(x²+y²)=24
x²+y²=12
(2)（x+y)²-（x-y)²=12

全部展开

(1)（x+y)²+（x-y)²=24
x²+2xy+y²+x²-2xy+y²=24
2(x²+y²)=24
x²+y²=12
(2)（x+y)²-（x-y)²=12
x²+2xy+y²-x²+2xy-y²=12
4xy=12
xy=3

收起

(x+y)^2-(x-y)^2
=x^2+2xy+y^2-(x^2-2xy-y^2)
=4xy=18-6=12
xy=3
x^2+y^2
=(x+y)^2-2xy
=18-2*3
=12