已知x+y=6,xy=7,试求x*x+y*y,x*x-y*y的值

问题描述:

已知x+y=6,xy=7,试求x*x+y*y,x*x-y*y的值

x²+y²=(x+y)²-2xy=36-14=22
(x-y)²=x²+y²-2xy=22-14=8
(x-y)=±√8=±2√2
x²-y²=(x-y)(x+y)=±12√2