x+y=32,x²-y²=48求xy

x+y=32,x²-y²=48求xy
x+y=32,x²-y²=48
求xy

x+y=32,x²-y²=48求xy
x+y=32,x²-y²=48
x-y = (x²-y²)÷ (x+y) = 48 ÷ 32 = 3/2
x= (32+3/2)÷2
= 16 又 4分之3
= 67 /4
y= 32 - 16 又 4分之3
= 15 又 4分之1
= 61/4
xy= 61x67 /16
= 16 分之 4087

x²-y²=(x+y)(x-y)=48
x+y=32代入
32(x-y)=48
x-y=3/2 (1)
x+y=32 (2)
(1)+(2)
2x=67/2 x=67/4
(2)-(1)
2y=61/2 y=61/4
xy=(67/4)(61/4)=4087/16

(x+y)(x-y)=32*(x-y)=48;x-y=3/2;
xy=1/4[(x+y)^2-(x-y)^2]=4087/16

x²－y²＝48
﹙x＋y﹚﹙x－y﹚＝48
x－y＝3/2
﹙x－y﹚²＝9/4
﹙x＋y﹚²－4xy＝9/4
32²－4xy＝9/4
xy＝﹙32²－9/4﹚/4＝4087/4