已知x-y=5,y-z=3,求x y z -xy-yz-xz的值
2个回答
展开全部
已知x-y=5,y-z=3,求x²+y²+z²-xy-yz-xz的值
x-y=5,y-z=2,则(x-y)+(y-z)=x-z=7,
x*x+y*y+z*z-xy-yz-zx
=x²+y²+z²-xy-yz-zx
=(1/2)*2*(x²+y²+z²-xy-yz-zx)
=(1/2)(2x²+2y²+2z²-2xy-2yz-2zx)
=(1/2)[(x-y)²+(y-z)²+(x-z)²]
=(1/2)(5²+2²+7²)
=(25+4+49)/2
=78/2
=39
x-y=5,y-z=2,则(x-y)+(y-z)=x-z=7,
x*x+y*y+z*z-xy-yz-zx
=x²+y²+z²-xy-yz-zx
=(1/2)*2*(x²+y²+z²-xy-yz-zx)
=(1/2)(2x²+2y²+2z²-2xy-2yz-2zx)
=(1/2)[(x-y)²+(y-z)²+(x-z)²]
=(1/2)(5²+2²+7²)
=(25+4+49)/2
=78/2
=39
本回答由提问者推荐
已赞过
已踩过<
你对这个回答的评价是？
推荐律师服务：
若未解决您的问题，请您详细描述您的问题，通过百度律临进行免费专业咨询
