已知:(x+y)²=4,(x-y)²=6,求x²+y²和xy的值.

已知:(x+y)²=4,(x-y)²=6,求x²+y²和xy的值.
已知:(x+y)²=4,(x-y)²=6,求x²+y²和xy的值.

已知:(x+y)²=4,(x-y)²=6,求x²+y²和xy的值.
x²+y²=【(x+y)²+(x-y)²】/2
=(4+6)÷2
=5
xy=【(x+y)²-(x+y)²】/4
=(4-6)/4
=-1/2

(x+y)²=4展开得x²+y²+2xy=4 ①
(x-y)²=6展开得x²+y²-2xy=6 ②
①+②得
2(x²+y²)=10
x²+y²=5
①-②得
4xy=-2
xy=-1/2

(x+y)²-(x-y)²=4xy
(x+y)²+(x-y)²=2x^2+2y^2
三者乃兄弟关系，切记即可

(x+y)²=4 (1)
(x-y)²=6 (2)
[(1)+(2)]/2： x² + y² = 5 (3)
[(1)-(2)]/4： xy = - 1/2 (4)