已知x+y=10,xy=4,求x²+y²和（x-y）²的值

已知x+y=10,xy=4,求x²+y²和（x-y）²的值
已知x+y=10,xy=4,求x²+y²和（x-y）²的值

已知x+y=10,xy=4,求x²+y²和（x-y）²的值
x²+y²
=(x+y)²-2xy
=10²-2*4
=100-8
=92
(x-y)²
=(x+y)²-4xy
=10²-4*4
=100-16
=84

x²＋y²＝﹙x＋y﹚²－2xy＝10²－8=92
﹙x－y﹚²＝﹙x＋y﹚²－4xy=10²－4×4=84